Simulation of resonance hyper-Rayleigh scattering of molecules and metal clusters using a time-dependent density functional theory approach

The Amsterdam Modeling Suite

In this paper, we present the Amsterdam Modeling Suite (AMS), a comprehensive software platform designed to support advanced molecular and materials simulations across a wide range of chemical and physical systems. AMS integrates cutting-edge quantum chemical methods, including Density Functional Theory (DFT) and time-dependent DFT, with molecular mechanics, fluid thermodynamics, machine learning techniques, and more, to enable multi-scale modeling of complex chemical systems. Its design philosophy allows for seamless coupling between components, facilitating simulations that range from small molecules to complex biomolecular and solid-state systems, making it a versatile tool for tackling interdisciplinary challenges, both in industry and in academia. The suite also emphasizes user accessibility, with an intuitive graphical interface, extensive scripting capabilities, and compatibility with high-performance computing environments.

Record-high hyperpolarizabilities in atomically precise single metal-doped silver nanoclusters

Recent developments in optical imaging techniques, particularly multi-photon excitation microscopy that allows studies of biological interactions at a deep cellular level, have motivated intensive research in developing multi-photon absorption fluorophores. Biological tissues are optically transparent in the near-infrared region. Therefore, fluorophores that can absorb light in the near-infrared (NIR) region by multi-photon absorption are particularly useful in bio-imaging. For instance, photoluminescence from ligand-protected gold nanoclusters has drawn extensive research interest in the past decade due to their bright, non-blinking, stable emission and tunability from the blue to the NIR emission. In this work, using the control of single metal doping on silver nanoclusters (Ag25 protected by thiolate SR = 2,4-dimethylbenzenethiol (DMBT) ligand), we aim to explore the effects of metal doping on the (photo)stability and nonlinear optical response of liganded nanoclusters. We study two-photon excited photoluminescence and the second harmonic response upon excitation in the NIR (780-950 nm) range. Particular emphasis is placed on the effect of metal doping on the second-order nonlinear optical scattering properties (first hyperpolarizability, β(2ω)) of Ag25 nanoclusters. In addition, β(2ω) values are one order higher than the one reported for Au25 nanoclusters and represent the largest values ever reported for ligand-protected nanoclusters. Such enhanced hyperpolarizability leads to a strong second harmonic response and renders them attractive targets in bioimaging.

Gauge-Invariant Excited-State Linear and Quadratic Response Properties within the Meta-Generalized Gradient Approximation

Gauge invariance is a fundamental symmetry connected to charge conservation and is widely accepted as indispensable for any electronic structure method. Hence, the gauge variance of the time-dependent kinetic energy density τ used in many meta-generalized gradient approximations (MGGAs) to the exchange-correlation (XC) functional presents a major obstacle for applying MGGAs within time-dependent density functional theory (TDDFT). Replacing τ by the gauge-invariant generalized kinetic energy density τ̂ significantly improves the accuracy of various functionals for vertical excitation energies [R. Grotjahn, F. Furche, and M. Kaupp. J. Chem. Phys. 2022, 157, 111102]. However, the dependence of the resulting current-MGGAs (cMGGAs) on the paramagnetic current density gives rise to new exchange-correlation kernels and hyper-kernels ignored in previous implementations of quadratic and higher-order response properties. Here we report the first implementation of cMGGAs and hybrid cMGGAs for excited-state gradients and dipole moments, as well as an extension to quadratic response properties including dynamic hyperpolarizabilities and two-photon absorption cross sections. In the first comprehensive benchmark study of MGGAs and cMGGAs for two-photon absorption cross sections, the M06-2X functional is found to be superior to the GGA hybrid PBE0. Additionally, two case studies from the literature for the practical prediction of nonlinear optical properties are revisited and potential advantages of hybrid (c)MGGAs compared to hybrid GGAs are discussed. The effect of restoring gauge invariance varies depending on the employed MGGA functional, the type of excitation, and the property under investigation: While some individual excited-state equilibrium structures are significantly affected, on average, these changes result in marginal improvements when compared against high-level reference data. Although the gauge-variant MGGA quadratic response properties are generally close to their gauge-invariant counterparts, the resulting errors are not bounded and significantly exceed typical method errors in some of the cases studied. Despite the limited effects seen in benchmark studies, gauge-invariant implementations of cMGGAs for excited-state properties are desirable from a fundamental perspective, entail little additional computational cost, and are necessary for response properties consistent with cMGGA linear response calculations such as excitation energies.

How do structural factors determine the linear and non-linear optical properties of fluorene-containing quadrupolar fluorophores? A theoretical answer

The linear and non-linear optical properties of the different components of a series of push–push and pull–pull quadrupolar fluorophore derivatives are investigated.

Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method

In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.

Influence of Membrane Phase on the Optical Properties of DPH

The fluorescent molecule diphenylhexatriene (DPH) has been often used in combination with fluorescence anisotropy measurements, yet little is known regarding the non-linear optical properties. In the current work, we focus on them and extend the application to fluorescence, while paying attention to the conformational versatility of DPH when it is embedded in different membrane phases. Extensive hybrid quantum mechanics/molecular mechanics calculations were performed to investigate the influence of the phase- and temperature-dependent lipid environment on the probe. Already, the transition dipole moments and one-photon absorption spectra obtained in the liquid ordered mixture of sphingomyelin (SM)-cholesterol (Chol) (2:1) differ largely from the ones calculated in the liquid disordered DOPC and solid gel DPPC membranes. Throughout the work, the molecular conformation in SM:Chol is found to differ from the other environments. The two-photon absorption spectra and the ones obtained by hyper-Rayleigh scattering depend strongly on the environment. Finally, a stringent comparison of the fluorescence anisotropy decay and the fluorescence lifetime confirm the use of DPH to gain information upon the surrounding lipids and lipid phases. DPH might thus open the possibility to detect and analyze different biological environments based on its absorption and emission properties.

Importance of double-resonance effects in two-photon absorption properties of Au25(SR)18. Chem Sci 2017. [PMID: 28626569 PMCID: PMC5471455 DOI: 10.1039/c7sc00968b]

We show that double-resonance effects for Au₂₅(SR)₁₈^– are less pronounced and do not lead to significantly enhanced two-photon absorption cross-sections.

The two-photon absorption (TPA) cross-sections of small thiolate-protected gold clusters have been shown to be much larger than typical small organic molecules. In comparison with larger nanoparticles, their TPA cross-sections per gold atom are also found to be larger. Theoretical simulations have suggested that the large enhancement of these TPA cross-sections comes from a one-photon double-resonance mechanism. However, it remains difficult to simulate TPA cross-sections of thiolate-protected gold clusters due to their large system size and a high density of states. In this work, we report a time-dependent density functional theory (TDDFT) study of the TPA spectra of the Au₂₅(SR)₁₈^– cluster based on a damped response theory formalism. Damped response theory enables a consistent treatment of on- and off-resonance molecular properties even for molecules with a high density of states, and thus is well-suited for studying the TPA properties of gold clusters. Our results indicate that the one- and two-photon double-resonance effect is much smaller than previously found, and thus is unlikely to be the main cause of the large TPA cross-sections found experimentally. The effect of symmetry breaking of the Au₂₅(SR)₁₈^– cluster due to the ligands on the TPA cross-sections has been studied and was found to only slightly increase the cross-section. Furthermore, by comparing with larger nanoparticles we find that the TPA cross-section per gold atom scales linearly with the diameter of the particles, and that the Kerr non-linear response of the Au₂₅(SR)₁₈^– cluster is on the same order as that of bulk gold films.

Alkyl-Nitrile Adlayers as Probes of Plasmonically Induced Electric Fields

Vibrational Stark shifts observed from mercaptoalkyl monolayers on surface enhanced Raman (SERS) active materials are reported to provide a direct measurement of the local electric field around plasmonic nanostructures. Adlayers of CN-, p-mercaptobenzonitrile, and n-mercaptobutylnitrile were adsorbed to a heterogeneous nanostructured Ag surface. The frequency of the CN moiety was observed to shift in a correlated fashion with the SERS intensity. These shifts are attributed to a vibrational Stark shift arising from rectification of the optical field, which gives rise to a DC potential on the surface. All three molecules showed CN Stark shifts on the plasmonic surfaces. P-mercaptobenzonitrile is observed to be a well-behaved probe of the electric field, providing a narrow spectral line, suggesting a more uniform orientation on the surface. The utility of p-mercaptobenzonitrile was demonstrated by successfully assessing the electric field between gold nanoparticles adsorbed to a monolayer of the nitrile on a flat gold surface. A model is presented where the Stark shift of the alkyl-nitrile probe can be correlated to optical field, providing an intensity independent measurement of the local electric field environment.