Finite lifetime effects on the polarizability within time-dependent density-functional theory

Efficient Simulation of Surface-Enhanced Raman Scattering with a Simplified Damped Response Theory

Theoretical studies on enhancement mechanisms of surface-enhanced Raman scattering (SERS) are usually carried out with full quantum mechanical methods to capture the specific interactions between molecules and substrates. However, due to the computational costs of methods like time-dependent density functional theory (TDDFT), simplified model systems are commonly adopted. In the framework of TDDFT, the damped response theory is usually invoked to give a unified description of both on- and off-resonance Raman spectra based on the calculation of polarizability derivatives. However, the computational costs of full TDDFT allow for modeling SERS spectra only using small metal clusters. In this work, we demonstrate the implementation of an efficient method that simplifies the damped response calculations for the simulation of both on- and off-resonance SERS spectra. This simplified damped response method is named as TBAOResponse. We first compare the absorption spectra of a regular small system calculated with TBAOResponse and full TDDFT to benchmark the new method. Then, we demonstrate the efficiency and accuracy of the new method by comparing the on- and off-resonance SERS spectra calculated with different methods. Compared to full TDDFT, while significant improvement of efficiency is achieved, the simplified damped response maintains good accuracy for SERS calculation. We further showcase the efficiency of TBAOResponse by calculating the SERS spectra for a system that is computationally demanding with full TDDFT. This new method is promising for modeling SERS systems when a full quantum mechanical description of both the substrate and the molecule is necessary.

Mixed atomistic-implicit quantum/classical approach to molecular nanoplasmonics

A multiscale quantum mechanical (QM)/classical approach is presented that is able to model the optical properties of complex nanostructures composed of a molecular system adsorbed on metal nanoparticles. The latter is described by a combined atomistic-continuum model, where the core is described using the implicit boundary element method (BEM) and the surface retains a fully atomistic picture and is treated employing the frequency-dependent fluctuating charge and fluctuating dipole (ωFQFμ) approach. The integrated QM/ωFQFμ-BEM model is numerically compared with state-of-the-art fully atomistic approaches, and the quality of the continuum/core partition is evaluated. The method is then extended to compute surface-enhanced Raman scattering within a time-dependent density functional theory framework.

Time-Dependent Resonant Inelastic X-ray Scattering of Pyrazine at the Nitrogen K-Edge: A Quantum Dynamics Approach

We calculate resonant inelastic X-ray scattering spectra of pyrazine at the nitrogen K-edge in the time domain including wavepacket dynamics in both the valence and core-excited state manifolds. Upon resonant excitation, we observe ultrafast non-adiabatic population transfer between core-excited states within the core-hole lifetime, leading to molecular symmetry distortions. Importantly, our time-domain approach inherently contains the ability to manipulate the dynamics of this process by detuning the excitation energy, which effectively shortens the scattering duration. We also explore the impact of pulsed incident X-ray radiation, which provides a foundation for state-of-the-art time-resolved experiments with coherent pulsed light sources.

Modeling the near-field effect on molecular excited states using the discrete interaction model/quantum mechanical method

Strong light-matter interactions significantly modify the optical properties of molecules in the vicinity of plasmonic metal nanoparticles. Since the dimension of the plasmonic cavity approaches that of the molecules, it is critical to explicitly describe the nanoparticle junctions. In this work, we use the discrete interaction model/quantum mechanical (DIM/QM) method to model the coupling between the plasmonic near-field and molecular excited states. DIM/QM is a combined electrodynamics/quantum mechanical model that uses an atomistic description of the nanoparticle. We extend the DIM/QM method to include the local field effects in the sum-over-state formalism of time-dependent density functional theory. As a test of the method, we study the interactions between small organic chromophores and metal nanoparticles. In particular, we examine how the inclusion of multiple electronic transitions and intermolecular interactions modify the coupling between molecules and nanoparticles. Using the sum-over-state formalism of DIM/QM, we show that two-state models break down when the plasmon excitation is detuned from the molecular excitations. To gain further insight, we compare the simple coupled-dipole model (CDM) with the DIM/QM model. We find that CDM works well for simple systems but fails when going beyond the single molecule or single nanoparticle cases. We also find that the coupling depends strongly on the site of the nanoparticle in which the chromophore couples to. Our work suggests the importance of explicitly describing the cavity to capture the atomistic level local field environment in which the molecule strongly couples to.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Introducing Bidirectional Axial Coordination into BiVO4 @Metal Phthalocyanine Core-Shell Photoanodes for Efficient Water Oxidation

Core-shell photoanodes have shown great potential for photoelectrochemical (PEC) water oxidation. However, the construction of a high-quality interface between the core and shell, as well as a highly catalytic surface, remains a challenge. Herein, guided by computation, we present a BiVO4 photoanode coated with ZnCoFe polyphthalocyanine using pyrazine as a coordination agent. The bidirectional axial coordination of pyrazine plays a dual role by facilitating intimate interfacial contact between BiVO4 and ZnCoFe polyphthalocyanine, as well as regulating the electron density and spin configuration of metal sites in ZnCoFe phthalocyanine, thereby promoting the potential-limiting step of *OOH desorption. The resulting photoanode displayed a high photocurrent density of 5.7±0.1 mA cm-2 at 1.23 VRHE . This study introduces a new approach for constructing core-shell photoanodes, and uncovers the key role of pyrazine axial coordination in modulating the catalytic activity of metal phthalocyanine.

Comparative Study of Vibrational Raman Optical Activity with Different Time-Dependent Density Functional Approximations: The VROA36 Database

A new database, VROA36, is introduced to investigate the performance of computational approaches for vibrational Raman optical activity (VROA) calculations. The database is composed of 36 molecules with known experimental VROA spectra. It includes 93 conformers. Normal modes calculated with B3LYP-D3(BJ)/def2-TZVP are used to compute the VROA spectra with four functionals, B3LYP-D3(BJ), ωB97X-D, M11, and optimally tuned LC-PBE, as well as several basis sets. SimROA indices and frequency scaling factors are used to compare calculated spectra with each other and with experimental data. The four functionals perform equally well independently of the basis set and usually achieve good agreement with the experimental data. For molecules in near- or at-resonance conditions, the inclusion of a complex (damped) linear response approach is important to obtain physically meaningful VROA intensities. The use of any of the tested functional approximations with the def2-SVPD Gaussian-type basis set, or a basis of similar flexibility, can be recommended for efficient and reliable theoretical VROA studies.

Intruder Peak-Free Transient Inner-Shell Spectra Using Real-Time Simulations

Real-time methods are convenient for simulating core-level absorption spectra but suffer from nonphysical intruder peaks when using atom-centered basis sets. In transient absorption spectra, these peaks exhibit highly nonphysical time-dependent modulations in their energies and oscillator strengths. In this paper, we address the origins of these intruder peaks and propose a straightforward and effective solution based on a filtered dipole operator. In combination with real-time time-dependent density functional theory (RT-TDDFT), we demonstrate how to compute intruder-free attosecond transient X-ray absorption spectra for the aminophenol (C₆H₇NO) oxygen and nitrogen K-edges and the α-quartz (SiO₂) silicon L-edge. Without filtering, the computed spectra are qualitatively wrong. This procedure is suitable for both static and transient inner-shell spectroscopy studies and can easily be implemented in a range of real-time methodologies.

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.

Exact-two-component block-localized wave function: A simple scheme for the automatic computation of relativistic ΔSCF

Block-localized wave function is a useful method for optimizing constrained determinants. In this article, we extend the generalized block-localized wave function technique to a relativistic two-component framework. Optimization of excited state determinants for two-component wave functions presents a unique challenge because the excited state manifold is often quite dense with degenerate states. Furthermore, we test the degree to which certain symmetries result naturally from the ΔSCF optimization such as time-reversal symmetry and symmetry with respect to the total angular momentum operator on a series of atomic systems. Variational optimizations may often break the symmetry in order to lower the overall energy, just as unrestricted Hartree-Fock breaks spin symmetry. Overall, we demonstrate that time-reversal symmetry is roughly maintained when using Hartree-Fock, but less so when using Kohn-Sham density functional theory. Additionally, maintaining total angular momentum symmetry appears to be system dependent and not guaranteed. Finally, we were able to trace the breaking of total angular momentum symmetry to the relaxation of core electrons.

Damped (linear) response theory within the resolution-of-identity coupled cluster singles and approximate doubles (RI-CC2) method

An implementation of a complex solver for the solution of the linear equations required to compute the complex response functions of damped response theory is presented for the resolution-of-identity (RI) coupled cluster singles and approximate doubles (CC2) method. The implementation uses a partitioned formulation that avoids the storage of double excitation amplitudes to make it applicable to large molecules. The solver is the keystone element for the development of the damped coupled cluster response formalism for linear and nonlinear effects in resonant frequency regions at the RI-CC2 level of theory. Illustrative results are reported for the one-photon absorption cross section of C₆₀, the electronic circular dichroism of n-helicenes (n = 5, 6, 7), and the C₆ dispersion coefficients of a set of selected organic molecules and fullerenes.

Relative contributions of Franck-Condon to Herzberg-Teller terms in charge transfer surface-enhanced Raman scattering spectroscopy

We have theoretically modeled charge transfer (CT) surface enhanced raman scattering (SERS) spectroscopy using pyridine bound to a planar Ag₆ metal nanocluster. CT states were determined by natural transition orbital hole-particle plots and CT distance D_CT and the amount of charge transferred q_CT indices. We first consider a resonance Raman (RR) model based on the Albrecht approach and calculate the ratio of the Herzberg-Teller (HT) B or C term to the Franck-Condon (FC) A term for a totally symmetric a₁ vibrational mode exciting in the lowest energy CT state. Using a dimensionless upper limit to the displacement factor ∆ = 0.05 in the FC term based on the examination of overtones in experimental spectra and a calculated HT coupling constant h_CT = 0.439 eV/Å(amu)^1/2 in the HT term, we calculated the scattering ratio of the HT to FC intensities as 147. This example indicated that for totally symmetric modes, the scattering intensity would all come from HT scattering. To further verify this result, we used the general time-dependent-RR formulation of Baiardi, Bloino, and Barone with the adiabatic Hessian model to calculate the FC, the Frank-Condon and Herzberg-Teller (FCHT), and the HT terms for pyridine in the C_2v Ag₆-pyridine complexes. For all cases we studied with pyridine in two orientations either parallel or perpendicular to the planar Ag₆ cluster, the HT terms, FCHT + HT, dominate the FC term in the CT RR spectrum. These results indicate that for CT SERS, the intensity of all the totally and non-totally symmetric vibrational modes should come from the HT effect.

Theoretical study of surface-enhanced Raman scattering mechanism of scandium-doped copper/silver clusters

Rare earth metals exhibit strong chemical activity and have many unique properties in the aspects of magnetic susceptibility, photo-absorption, catalytic activity and electrical property. Precious metals have strong chemical stability and great surface-enhanced Raman scattering (SERS) enhancing activity, providing a good platform for detecting SERS signals from molecules. Combining precious metals with rare earth metals could form new composite materials, providing more possibilities for SERS substrates. In this work, the SERS and absorption spectra of the probe molecule adsorbed on scandium-doped silver/copper clusters are theoretically simulated by time-dependent density functional theory. The contributions of charge-transfer (CT) enhancement and electromagnetic enhancement are treated uniformly in calculations based on a short-time approximation for the Raman scattering cross-section, and distinguished by using visualization of electron transitions. The largest Raman enhancement factor of the probe molecule adsorbed on Sc@Cu₇ and Sc@Ag₇ alloy clusters could reach the order of 10⁵, due to the enhancement of resonance excitation to the CT transition. The factors influencing SERS are systematically investigated, including the composition of the substrate, local chemical environment of the binding site, form of electron transition, oscillator strength of excitation and excitation wavelength.

Direct Surface Enhanced Raman Spectroscopic Detection of Cortisol at Physiological Concentrations

Cortisol is an important steroid hormone in human physiology. Variations or abnormalities in the physiological cortisol levels control acute and chronic stress response, as well as contribute to diseases and syndromes including Addison's disease and Cushing syndrome. The ability to monitor cortisol levels in the physiological range is key in diagnosis and monitoring of these conditions, where current methodology for determination of cortisol levels relies on instrumentation that requires extensive sample preparation, long run times, and is destructive to the sample. Raman spectroscopy provides rapid sample analysis with relatively simple instrumentation; however, Raman spectroscopy is an inherently weak technique. To provide an enhanced Raman signal, we use surface enhanced Raman spectroscopy (SERS) which utilizes oscillating electric fields of metal nanoparticles, enhancing the overall electric field and therefore resulting in an enhanced signal. We demonstrate SERS-based detection of cortisol in the physiologically relevant range using colloidal silver nanoparticles in ethanolic solutions and bovine serum albumin. The SERS spectra obtained in an ethanol matrix demonstrate a sigmoidal concentration response over the physiologically relevant concentration range, with a limit of detection established at 177 nM. Analysis of cortisol solutions in a complex matrix (bovine serum albumin in phosphate buffered saline) is also demonstrated through the use of principal components analysis, a multivariate technique, which shows the separation of cortisol in a linear fashion with respect to cortisol concentration.

Core–valence-separated coupled-cluster-singles-and-doubles complex-polarization-propagator approach to X-ray spectroscopies

The iterative subspace algorithm to solve the CCSD complex linear response equations has been modified to include a core–valence separation projection step to overcome convergence problems. Illustrative results are reported for XAS, XCD, XES and RIXS.

How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core–valence separation

We present a novel approach with robust convergence of the response equations for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework.

Roles of silver nanoclusters in surface-enhanced Raman spectroscopy

The cause for the huge enhancement factors of surface-enhanced Raman spectroscopy (SERS) by the addition of small silver nanoclusters is theoretically investigated by focusing on the difference between resonance Raman activity and surface plasmon effects. First, the resonance and off-resonance Raman spectra are calculated using the incident light wavenumbers of the low-lying charge transfer excitations for the surface (S) and vertex (V) complexes of the pyridine molecule attaching to three small silver nanoclusters: Ag₅, Ag₁₀, and Ag₂₀. As a result, it is found that the incident radiation dramatically increases the resonance Raman activities with the enhancement factors up to 10¹². This indicates that the resonance Raman effects are dominant in the enhancement factors of SERS, at least when to use small silver clusters. It is also found that the resonance Raman spectra significantly depend on the adsorption sites given in S or V complexes, and on the inclusion or exclusion of the long-range correction for density functional theory, irrespective of the size of the silver clusters. The electromagnetic field enhancement effects called "surface plasmon effects" are also examined for the Ag₂₀ cluster to confirm this conclusion. Consequently, the enhancement in the electric field is roughly evaluated as less than one for the static polarizability of this small cluster. It is, therefore, concluded that the resonance Raman activity effect is dominant in the huge SERS enhancement factors for, at least, small silver nanoclusters.

Computing Bulk Phase Resonance Raman Spectra from ab Initio Molecular Dynamics and Real-Time TDDFT

We present our novel approach for computing resonance Raman (RR) spectra of periodic bulk phase systems from ab initio molecular dynamics, including solvent influence and some anharmonic effects. Based on real-time time-dependent density functional theory, we obtain the RR spectra for all laser wavelengths in one pass. We compute the RR spectrum of uracil in aqueous solution, which is in good agreement with experiment. This is the first simulation of a bulk phase RR spectrum.

Ehrenfest+R dynamics. II. A semiclassical QED framework for Raman scattering

In Paper I [Chen et al., J. Chem. Phys. 150, 044102 (2019)], we introduced Ehrenfest+R dynamics for a two-level system and showed how spontaneous emission can be heuristically included such that, after averaging over an ensemble of Ehrenfest+R trajectories, one can recover both coherent and incoherent electromagnetic fields. In the present paper, we now show that Ehrenfest+R dynamics can also correctly describe Raman scattering, whose features are completely absent from standard Ehrenfest dynamics. Ehrenfest+R dynamics appear to be quantitatively accurate both for resonant and off-resonant Raman signals, as compared with Kramers-Heisenberg-Dirac theory.

A Discrete Interaction Model/Quantum Mechanical Method for Simulating Plasmon-Enhanced Two-Photon Absorption

In this work, we extend the discrete interaction model/quantum mechanical (DIM/QM) method to simulate plasmon-enhanced two-photon absorption (PETPA). The metal nanoparticle is treated atomistically by means of electrodynamics, while the molecule is described using damped cubic response theory within a time-dependent density functional theory framework. Using DIM/QM, we study the PETPA of para-nitroaniline ( p-NA) with a focus on the local and image field effects, the molecular orientation effects, and the molecule-nanoparticle distance effects. Our findings show that the enhancement is more complex than the simple | E|⁴ enhancement mechanism, where | E| is the local field at the position of the molecule. Because of specific interactions with the nanoparticle, we find that a TPA dark state of p-NA can be significantly enhanced through a coupling with the plasmon excitation. The results presented in this work illustrate that the coupling between molecular excitations and plasmons can give rise to unusual and complex behavior in nonlinear spectroscopy that cannot simply be understood by considering the optical properties of the individual molecules and nanoparticles separately. The method presented here provides detailed insights into the enhancement of nonlinear optical properties of molecules coupled to plasmonic nanoparticles.

Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

Three meso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods. These species are experimentally known to display a prominent reverse saturable absorption feature between the Q and B bands of the ground-state absorption (GSA), which has been attributed to increased excited-state absorption (ESA) relative to GSA. A recently developed RT-TDDFT based method for calculating ESA from a LR-TDDFT density was utilized with eight exchange-correlation functionals (BLYP, PBE, B3LYP, CAM-B3LYP, PBE0, M06, BHLYP, and BHandH) and contrasted with calculations of ESA using QR-TDDFT with five exchange-correlation functionals (BLYP, B3LYP, CAM-B3LYP, BHLYP, and BHandH). This allowed for comparison between functionals with varying amounts of exact exchange as well as between the ability of RT-TDDFT and QR-TDDFT to reproduce OL behavior in porphyrin systems. The absorption peak positions and intensities for GSA and ESA are significantly impacted by the choice of DFT functional, with the most critical factor identified as the amount of exact exchange in the functional form. Calculating ESA with QR-TDDFT is found to be significantly more sensitive to the amount of exact exchange than GSA and ESA with RT-TDDFT, as well as GSA with LR-TDDFT. An analogous behavior is also demonstrated for the polycyclic aromatic hydrocarbon coronene. This is problematic when using the same approximate functional for calculation of both GSA and ESA, as the LR- and QR-TDDFT excitation energies will not have similar errors. Overall, the RT-TDDFT method with hybrid functionals reproduces the OL features for the porphyrin systems studied here and is a viable computational approach for efficient screening of molecular complexes for OL properties.

Atomic-Scale Lightning Rod Effect in Plasmonic Picocavities: A Classical View to a Quantum Effect

Plasmonic gaps are known to produce nanoscale localization and enhancement of optical fields, providing small effective mode volumes of about a few hundred nm³. Atomistic quantum calculations based on time-dependent density functional theory reveal the effect of subnanometric localization of electromagnetic fields due to the presence of atomic-scale features at the interfaces of plasmonic gaps. Using a classical model, we explain this as a nonresonant lightning rod effect at the atomic scale that produces an extra enhancement over that of the plasmonic background. The near-field distribution of atomic-scale hot spots around atomic features is robust against dynamical screening and spill-out effects and follows the potential landscape determined by the electron density around the atomic sites. A detailed comparison of the field distribution around atomic hot spots from full quantum atomistic calculations and from the local classical approach considering the geometrical profile of the atoms' electronic density validates the use of a classical framework to determine the effective mode volume in these extreme subnanometric optical cavities. This finding is of practical importance for the community of surface-enhanced molecular spectroscopy and quantum nanophotonics, as it provides an adequate description of the local electromagnetic fields around atomic-scale features with use of simplified classical methods.

Probing Intermolecular Vibrational Symmetry Breaking in Self-Assembled Monolayers with Ultrahigh Vacuum Tip-Enhanced Raman Spectroscopy

Ultrahigh vacuum tip-enhanced Raman spectroscopy (UHV-TERS) combines the atomic-scale imaging capability of scanning probe microscopy with the single-molecule chemical sensitivity and structural specificity of surface-enhanced Raman spectroscopy. Here, we use these techniques in combination with theory to reveal insights into the influence of intermolecular interactions on the vibrational spectra of a N-N'-bis(2,6-diisopropylphenyl)-perylene-3,4:9,10-bis(dicarboximide) (PDI) self-assembled monolayer adsorbed on single-crystal Ag substrates at room temperature. In particular, we have revealed the lifting of a vibrational degeneracy of a mode of PDI on Ag(111) and Ag(100) surfaces, with the most strongly perturbed mode being that associated with the largest vibrational amplitude on the periphery of the molecule. This work demonstrates that UHV-TERS enables direct measurement of molecule-molecule interaction at nanoscale. We anticipate that this information will advance the fundamental understanding of the most important effect of intermolecular interactions on the vibrational modes of surface-bound molecules.

SERRS and absorption spectra of pyridine on Au m Ag n (m + n = 6) bimetallic nanoclusters: substrate composition and applied electric field effects

Surface-enhanced Raman scattering (SERS) and absorption spectra of the pyridine molecule adsorbed on Au _m Ag _n (m + n = 6) bimetallic clusters are theoretically investigated by time-dependent density functional theory. The contributions of static chemical enhancement to the ground-state system are analyzed, and the static Raman intensity of Py-Au _m Ag _n complexes are enhanced by an order of 10. A method of visualization on charge transfer is used to distinguish the contributions of charge-transfer enhancement and electromagnetic enhancement. The intensity of surface-enhanced resonance Raman scattering (SERRS) spectroscopy of Py-Au _m Ag _n is strongly enhanced by an order of 10³-10⁵, compared to the static Raman intensity of pyridine. The influence of the static external electric field on SERS is investigated by calculating the optical properties of the Py-Au₃Ag₃ complex. The intensity of SERRS spectra and normal Raman spectra can be significantly enhanced by the positive electric fields, and the intensities of specific Raman vibrational modes could be selectively enhanced or weakened by tuning the direction and strength of the static electric field applied on Py-Au₃Ag₃.

Nanostructured organic semiconductor films for molecular detection with surface-enhanced Raman spectroscopy

π-Conjugated organic semiconductors have been explored in several optoelectronic devices, yet their use in molecular detection as surface-enhanced Raman spectroscopy (SERS)-active platforms is unknown. Herein, we demonstrate that SERS-active, superhydrophobic and ivy-like nanostructured films of a molecular semiconductor, α,ω-diperfluorohexylquaterthiophene (DFH-4T), can be easily fabricated by vapour deposition. DFH-4T films without any additional plasmonic layer exhibit unprecedented Raman signal enhancements up to 3.4 × 10³ for the probe molecule methylene blue. The combination of quantum mechanical computations, comparative experiments with a fluorocarbon-free α,ω-dihexylquaterthiophene (DH-4T), and thin-film microstructural analysis demonstrates the fundamental roles of the π-conjugated core fluorocarbon substitution and the unique DFH-4T film morphology governing the SERS response. Furthermore, Raman signal enhancements up to ∼10¹⁰ and sub-zeptomole (<10^-21 mole) analyte detection were accomplished by coating the DFH-4T films with a thin gold layer. Our results offer important guidance for the molecular design of SERS-active organic semiconductors and easily fabricable SERS platforms for ultrasensitive trace analysis.

X-ray circular dichroism signals: a unique probe of local molecular chirality

Core-resonant circular dichroism (CD) signals are induced by molecular chirality and vanish for achiral molecules and racemic mixtures. The highly localized nature of core excitations makes them ideal probes of local chirality within molecules. Simulations of the circular dichroism spectra of several molecular families illustrate how these signals vary with the electronic coupling to substitution groups, the distance between the X-ray chromophore and the chiral center, geometry, and chemical structure. Clear insight into the molecular structure is obtained through analysis of the X-ray CD spectra.

Single-Molecule Imaging Using Atomistic Near-Field Tip-Enhanced Raman Spectroscopy

Advances in tip-enhanced Raman spectroscopy (TERS) have demonstrated ultrahigh spatial resolution so that the vibrational modes of individual molecules can be visualized. The spatial resolution of TERS is determined by the confinement of the plasmon-induced field in the junction; however, the conditions necessary for achieving the high spatial confinement required for imaging individual molecules are not fully understood. Here, we present a systematic theoretical study of TERS imaging of single molecules, using a hybrid atomistic electrodynamics-quantum mechanical method. This approach provides a consistent treatment of the molecule and the plasmonic near field under conditions where they cannot be treated separately. In our simulations, we demonstrate that TERS is capable of resolving intricate molecule vibrations with atomic resolution, although we find that TERS images are extremely sensitive to the near field in the junction. Achieving the atomic resolution requires the near field to be confined within a few ångstroms in diameter and the near-field focal plane to be in the molecule plane. Furthermore, we demonstrate that the traditional surface selection rule of Raman spectroscopy is altered due to the significant field confinement that leads to significant field-gradient effects in the Raman scattering. This work provides insights into single-molecule imaging based on TERS and Raman scattering of molecules in nanojunctions with atomic dimensions.

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.

Strong Dipolar Effects on an Octupolar Luminiscent Chromophore: Implications on their Linear and Nonlinear Optical Properties

Design parameters derived from structure-property relationships play a very important role in the development of efficient molecular-based functional materials with optical properties. Here, we report on the linear and nonlinear optical properties of a fluorene-derived dipolar system (DS) and its octupolar analogue (OS), in which donor and acceptor groups are connected by a phenylacetylene linkage, as a strategy to increase the number of delocalized electrons in the π-conjugated system. The optical nonlinear response was analyzed in detail by experimental and theoretical methods, showing that, in the octupolar system OS, the dipolar effects induced a strong two-photon absorption process whose magnitude is as large as 2210 GM at infrared wavelengths. Solvatochromism studies were implemented to obtain further insight on the charge transfer process. We found that the triple bond plays a fundamental role in the linear and nonlinear optical responses. The strong solvatochromism behavior in DS and OS was analyzed by using four empirical solvent scales, namely Lippert-Mataga, Kamlet-Taft, Catalán, and the recently proposed scale of Laurence et al., finding consistent results of strong solvent polarizability and viscosity dependence. Finally, the role of the acceptor groups was further studied by synthesizing the analogous compound 2DS, having no acceptor group.

Nanoscale Chemical Imaging of a Dynamic Molecular Phase Boundary with Ultrahigh Vacuum Tip-Enhanced Raman Spectroscopy

Nanoscale chemical imaging of a dynamic molecular phase boundary has broad implications for a range of problems in catalysis, surface science, and molecular electronics. While scanning probe microscopy (SPM) is commonly used to study molecular phase boundaries, its information content can be severely compromised by surface diffusion, irregular packing, or three-dimensional adsorbate geometry. Here, we demonstrate the simultaneous chemical and structural analysis of N-N'-bis(2,6-diisopropylphenyl)-1,7-(4'-t-butylphenoxy)perylene-3,4:9,10-bis(dicarboximide) (PPDI) molecules by UHV tip-enhanced Raman spectroscopy. Both condensed and diffusing domains of PPDI coexist on Ag(100) at room temperature. Through comparison with time-dependent density functional theory simulations, we unravel the orientation of PPDI molecules at the dynamic molecular domain boundary with unprecedented ∼4 nm spatial resolution.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.

Infrared and Raman Spectroscopy from Ab Initio Molecular Dynamics and Static Normal Mode Analysis: The C-H Region of DMSO as a Case Study

Carbon-hydrogen (C-H) vibration modes serve as key probes in the chemical identification of hydrocarbons and in vibrational sum-frequency generation spectroscopy of hydrocarbons at the liquid/gas interface. Their assignments pose a challenge from a theoretical viewpoint. In this work, we present a detailed study of the C-H stretching region of dimethyl sulfoxide using a new ab initio molecular dynamics (AIMD) module that we have implemented in NWChem. Through a combination of AIMD simulations and static normal mode analysis, we interpret experimental infrared and Raman spectra and explore the role of anharmonic effects in this system. Comprehensive anharmonic normal mode analysis of the C-H stretching region casts doubt upon previous experimental assignments of the shoulder on the symmetric C-H stretching peak. In addition, our AIMD simulations also show significant broadening of the in-phase symmetric C-H stretching resonance, which suggests that the experimentally observed shoulder is due to thermal broadening of the symmetric stretching resonance.