Vibronic coupling simulations for linear and nonlinear optical processes: Theory

Two-Photon Absorption Strengths of Small Molecules: Reference CC3 Values and Benchmarks

We present a large dataset of highly accurate two-photon transition strengths (δTPA) determined for standard small molecules. Our reference values have been calculated using the quadratic response implementation of the third-order coupled cluster method including iterative triples (Q-CC3). The aug-cc-pVTZ atomic basis set is used for molecules with up to five non-hydrogen atoms, while larger molecules are assessed with aug-cc-pVDZ; the differences due to the basis sets are discussed. This dataset, encompassing 82 singlet transitions of various characters (Rydberg, valence, and double excitations), enables a comprehensive benchmark of smaller basis sets and alternative wavefunction methods when Q-CC3 calculations become beyond reach as well as time-dependent density functional theory (TD-DFT) approaches. The evaluated wavefunction methods include quadratic response and equation-of-motion CCSD approximations, Q-CC2, and second-order algebraic diagrammatic construction in its intermediate state representation (I-ADC2). In the TD-DFT framework, a set of five commonly used exchange-correlation functionals are evaluted. This extensive analysis provides a quantitative assessment of these methods, revealing how different system sizes, response intensities, and types of transitions affect their performances.

Calculating absorption and fluorescence spectra for chromophores in solution with ensemble Franck-Condon methods

Accurately modeling absorption and fluorescence spectra for molecules in solution poses a challenge due to the need to incorporate both vibronic and environmental effects, as well as the necessity of accurate excited state electronic structure calculations. Nuclear ensemble approaches capture explicit environmental effects, Franck-Condon methods capture vibronic effects, and recently introduced ensemble-Franck-Condon approaches combine the advantages of both methods. In this study, we present and analyze simulated absorption and fluorescence spectra generated with combined ensemble-Franck-Condon approaches for three chromophore-solvent systems and compare them to standard ensemble and Franck-Condon spectra, as well as to the experiment. Employing configurations obtained from ground and excited state ab initio molecular dynamics, three combined ensemble-Franck-Condon approaches are directly compared to each other to assess the accuracy and relative computational time. We find that the approach employing an average finite-temperature Franck-Condon line shape generates spectra nearly identical to the direct summation of an ensemble of Franck-Condon spectra at one-fourth of the computational cost. We analyze how the spectral simulation method, as well as the level of electronic structure theory, affects spectral line shapes and associated Stokes shifts for 7-nitrobenz-2-oxa-1,3-diazol-4-yl and Nile red in dimethyl sulfoxide and 7-methoxy coumarin-4-acetic acid in methanol. For the first time, our studies show the capability of combined ensemble-Franck-Condon methods for both absorption and fluorescence spectroscopy and provide a powerful tool for simulating linear optical spectra.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

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.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck-Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ^★ S₀ → S₁ transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm^-1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

On-off-on Control of Molecular Inversion Symmetry via Multi-stage Protonation: Elucidating Vibronic Laporte Rule

The Laporte rule dictates that one- and two-photon absorption spectra of inversion-symmetric molecules should display alternatively forbidden electronic transitions; however, for organic fluorophores, drawing clear distinction between the symmetric- and non-inversion symmetric two-photon spectra is often obscured due to prevalent vibronic interactions. We take advantage of consecutive single- and double-protonation to break and then reconstitute inversion symmetry in a nominally symmetric diketopyrrolopyrrole, causing large changes in two-photon absorption. By performing detailed one- and two-photon titration experiments, with supporting quantum-chemical model calculations, we explain how certain low-frequency vibrational modes may lead to apparent deviations from the strict Laporte rule. As a result, the system may be indeed considered as an on-off-on inversion symmetry switch, opening new avenues for two-photon sensing applications.

All-experimental analysis of doubly resonant sum-frequency generation spectra for Franck–Condon and Herzberg–Teller vibronic modes

The transform technique applied to the analysis of doubly resonant sum-frequency generation (DR-SFG) spectra is extended to include Herzberg–Teller (HT) vibronic modes. The experimentally measured overlap spectral function generates all the energy resonant amplitudes of the DR-SFG excitation function for both Franck–Condon (FC) and HT modes. When FC modes dominate the DR-SFG spectra, a methodology is provided to perform efficient curve fitting and orientation analysis in order to extract FC activities of the various vibration modes from experimental spectra with the help of a molecular model. Determination of the FC or HT natures of the vibration modes from DR-SFG data is also shown to be possible through their visible line shapes with an appropriate choice of polarizations. As an example, experimental DR-SFG data suggest that a known HT-active mode in the vibronic structure of Rhodamine 6G monomers exhibits a FC behavior in molecular aggregates.

Doubly Resonant Sum-Frequency Vibrational Spectroscopy of 1,1'-Bi-2-naphthol Chiral Solutions Due to the Nonadiabatic Effect

Second-order nonlinear spectroscopy is a powerful tool in exploring significant physical and chemical characteristics at various interfaces and on chiral systems. We present a method of computing the nonadiabatic couplings between the different excited electronic states with time-dependent density functional theory and then study doubly resonant sum-frequency vibrational spectroscopy (SFVS) of chiral solutions due to the nonadiabatic, Franck-Condon, and Herzberg-Teller (HT) effects. The calculations for R-1,1'-bi-2-naphthol show that the theoretical spectra agree with experiment, and the nonadiabatic corrections are comparable with the HT terms or even larger for some vibrational modes, which is different from the mechanism of SFVS off electronic resonance. Doubly resonant SFVS may be a useful method of studying the nonradiative transition and nonadiabatic effect between the excited electronic states.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor–acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure–property studies across large series of dipolar compounds.

Optical Images of Molecular Vibronic Couplings from Tip-Enhanced Fluorescence Excitation Spectroscopy

Tip-based photoemission spectroscopic techniques have now achieved subnanometer resolution that allows visualization of the chemical structure and even the ground-state vibrational modes of a single molecule. However, the ability to visualize the interplay between electronic and nuclear motions of excited states, i.e., vibronic couplings, is yet to be explored. Herein, we theoretically propose a new technique, namely, tip-enhanced fluorescence excitation (TEFE). TEFE takes advantage of the highly confined plasmonic field and thus can offer a possibility to directly visualize the vibronic effect of a single molecule in real space for arbitrary excited states in a given energy window. Numerical simulations for a single porphine molecule confirm that vibronic couplings originating from Herzberg-Teller (HT) active modes can be visually identified. TEFE further enables high-order vibrational transitions that are normally suppressed in the other plasmon-based processes. Images of the combination vibrational transitions have the same pattern as that of their parental HT active mode's fundamental transition, providing a direct protocol for measurements of the activity of Franck-Condon modes of selected excited states. These findings strongly suggest that TEFE is a powerful strategy to identify the involvement of molecular moieties in the complicated electron-nuclear interactions of the excited states at the single-molecule level.

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.

Sum-over-state expressions including second-order Herzberg-Teller effects for the calculation of absorption and resonance Raman intensities

The sum-over-state expressions are derived to calculate the second-order Herzberg-Teller (HT) effects in absorption and resonance Raman spectroscopies. These effects depend on the second derivatives of the transition dipole moment with respect to the vibrational coordinates. The method is applied to the molecule of 1,3-butadiene using density functional theory calculations. It is found that the second-order HT effects are significant for both absorption and resonance Raman intensities, and that the calculated spectra are in good agreement with the experimental data. The second-order HT effects originate from diagonal elements of the second derivatives matrix, whereas non-diagonal elements have a negligible impact on the intensities of 1,3-butadiene.

All-experimental analysis of doubly resonant sum-frequency generation spectra: Application to aggregated rhodamine films

A new method is proposed to analyze Doubly Resonant infrared-visible Sum-Frequency Generation (DR-SFG) spectra. Based on the transform technique, this approach is free from assumptions about vibronic modes, energies, or line widths and accurately captures through the overlap spectral function all required aspects of the vibronic structure from simple experimental linear absorption spectra. Details and implementation of the method are provided along with three examples treating rhodamine thin films about one monolayer thick. The technique leads to a perfect agreement between experiment and simulations of the visible DR-SFG line shapes, even in the case of complex intermolecular interactions resulting from J-aggregated chromophores in heterogeneous films. For films with mixed H- and J-aggregates, separation of their responses shows that the J-aggregate DR-SFG response is dominant. Our analysis also accounts for the unexplained results published in the early times of DR-SFG experiments.

Recent advances and perspectives in photo-induced enhanced Raman spectroscopy

Phototreatment is at the leading edge of a research hot topic as a driving force for structural transformation, spectral and electromagnetism improvements, and the functional performance of nanomaterials. Light irradiation can excite surface plasmons in noble metal nanoparticles, create electron-hole pairs, and produce charge transfer in semiconductor substrates, which have led to it being widely used in surface-enhanced Raman spectroscopy (SERS) for life sciences, environmental protection, and biological analysis. Photo-induced enhanced Raman spectroscopy (PIERS) is a new technology developed on the basis of traditional SERS and has proven to be an efficient way to resolve several critical challenges thanks to its incomparable superiority for incontiguous operation, efficient charge separation and enrichment, and a large signal enhancement for a wide range of biomolecules at the trace level. This makes PIERS a powerful technique with very appealing and promising applications in various branches of analytical science. In this review, the enhancement mechanisms of PIERS are analyzed in comparison with SERS. Afterward, the parameters influencing the enhancement of PIERS, including the substrate, light irradiation, and relaxation are discussed in detail. Finally, some perspectives on further developments of PIERS are exemplified. The PIERS technique will continue to evolve and grow with new developments and its successful application in bioanalysis and life sciences.

Surface-enhanced hyper-Raman scattering of Rhodamine 6G isotopologues: Assignment of lower vibrational frequencies

We report a comprehensive experimental and theoretical study of the lower-wavenumber vibrational modes in the surface-enhanced hyper-Raman scattering (SEHRS) of Rhodamine 6G (R6G) and its isotopologue R6G-d4. Measurements acquired on-resonance with two different electronic states, S₁ and S₂, are compared to the time-dependent density functional theory computations of the resonance hyper-Raman spectra and electrodynamics-quantum mechanical computations of the SEHRS spectra on-resonance with S₁ and S₂. After accounting for surface orientation, we find excellent agreement between experiment and theory for both R6G and its isotopologue. We then present a detailed analysis of the complex vibronic coupling effects in R6G and the importance of surface orientation for characterizing the system. This combination of theory and experiment allows, for the first time, an unambiguous assignment of lower-wavenumber vibrational modes of R6G and its isotopologue R6G-d4.

Herzberg-Teller Effect Predominates in Sum-Frequency Vibrational Spectroscopy of Limonene Chiral Liquids

We theoretically study the bulk sum-frequency vibrational spectroscopy of chiral liquids under the influence of the Franck-Condon, Herzberg-Teller, and nonadiabatic effects. With quantum chemistry computations we calculate the chiral spectra for the R-limonene molecule. When we compare the theoretical and experimental spectra, we find that the Herzberg-Teller effect under the Born-Oppenheimer approximation, instead of the nonadiabatic effect, predominates in the chiral spectra.

Time-Dependent Formulation of Resonance Raman Optical Activity Spectroscopy

In this work, we extend the theoretical framework recently developed for the simulation of resonance Raman (RR) spectra of medium-to-large sized systems to its chiral counterpart, namely, resonance Raman optical activity (RROA). The theory is based on a time-dependent (TD) formulation, with the transition tensors obtained as half-Fourier transforms of the appropriate cross-correlation functions. The implementation has been kept as general as possible, supporting adiabatic and vertical models for the PES representation, both in Cartesian and internal coordinates, with the possible inclusion of Herzberg-Teller (HT) effects. Thanks to the integration of this TD-RROA procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects can be included in an effective way. The implementation is validated on one of the smallest chiral molecule (methyloxirane). Practical applications are illustrated with three medium-size organic molecules (naproxen-OCD₃, quinidine and 2-Br-hexahelicene), whose simulated spectra are compared to the corresponding experimental data.

Nonempirical Simulations of Inhomogeneous Broadening of Electronic Transitions in Solution: Predicting Band Shapes in One- and Two-Photon Absorption Spectra of Chalcones

We have examined several approaches relying on the Polarizable Embedding (PE) scheme to predict optical band shapes for two chalcone molecules in methanol solution. The PE-TDDFT and PERI-CC2 methods were combined with molecular dynamics simulations, where the solute geometry was kept either as rigid, flexible or partly-flexible (restrained) body. The first approach, termed RBMD-PE-TDDFT, was employed to estimate the inhomogeneous broadening for subsequent convolution with the vibrationally-resolved spectra of the molecule in solution determined quantum-mechanically (QM). As demonstrated, the RBMD-PE-TDDFT/QM-PCM approach delivers accurate band widths, also reproducing their correct asymmetric shapes. Further refinement can be obtained by the estimation of the inhomogeneous broadening using the RBMD-PERI-CC2 method. On the other hand, the remaining two approaches (FBMD-PE-TDDFT and ResBMD-PE-TDDFT), which lack quantum-mechanical treatment of molecular vibrations, lead to underestimated band widths. In this study, we also proposed a simple strategy regarding the rapid selection of the exchange-correlation functional for the simulations of vibrationally-resolved one- and two-photon absorption spectra based on two easy-to-compute metrics.

Surface-Enhanced Resonance Hyper-Raman Scattering Elucidates the Molecular Orientation of Rhodamine 6G on Silver Colloids

Herein, we utilize surface-enhanced hyper-Raman scattering (SEHRS) under resonance conditions to probe the adsorbate geometry of rhodamine 6G (R6G) on silver colloids. Our results show resonance SEHRS is highly sensitive to molecular orientation due to non-Condon effects, which do not appear in its linear counterpart surface-enhanced Raman scattering. Comparisons between simulated and measured SEHRS spectra reveal R6G adsorbs mostly perpendicular to the nanoparticle surface along the ethylamine groups with the xanthene ring oriented edgewise. Our results expand upon previous studies that rely on indirect, qualitative probes of R6G's orientation on plasmonic substrates. More importantly, this work represents the first determination of adsorbate geometry by SEHRS and opens up the possibility to study the orientation of single molecules in complex, plasmonic environments.

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.

Core-Shell Nanoparticle-Enhanced Raman Spectroscopy

Core-shell nanoparticles are at the leading edge of the hot research topics and offer a wide range of applications in optics, biomedicine, environmental science, materials, catalysis, energy, and so forth, due to their excellent properties such as versatility, tunability, and stability. They have attracted enormous interest attributed to their dramatically tunable physicochemical features. Plasmonic core-shell nanomaterials are extensively used in surface-enhanced vibrational spectroscopies, in particular, surface-enhanced Raman spectroscopy (SERS), due to the unique localized surface plasmon resonance (LSPR) property. This review provides a comprehensive overview of core-shell nanoparticles in the context of fundamental and application aspects of SERS and discusses numerous classes of core-shell nanoparticles with their unique strategies and functions. Further, herein we also introduce the concept of shell-isolated nanoparticle-enhanced Raman spectroscopy (SHINERS) in detail because it overcomes the long-standing limitations of material and morphology generality encountered in traditional SERS. We then explain the SERS-enhancement mechanism with core-shell nanoparticles, as well as three generations of SERS hotspots for surface analysis of materials. To provide a clear view for readers, we summarize various approaches for the synthesis of core-shell nanoparticles and their applications in SERS, such as electrochemistry, bioanalysis, food safety, environmental safety, cultural heritage, materials, catalysis, and energy storage and conversion. Finally, we exemplify about the future developments in new core-shell nanomaterials with different functionalities for SERS and other surface-enhanced spectroscopies.

Theory of Linear and Nonlinear Surface-Enhanced Vibrational Spectroscopies

The vibrational spectroscopy of molecules adsorbed on metal nanoparticles can be enhanced by many orders of magnitude so that the detection and identification of single molecules are possible. The enhancement of most linear and nonlinear vibrational spectroscopies has been demonstrated. In this review, we discuss theoretical approaches to understanding linear and nonlinear surface-enhanced vibrational spectroscopies. A unified description of enhancement mechanisms classified as either electromagnetic or chemical in nature is presented. Emphasis is placed on understanding the spectral changes necessary for interpretation of linear and nonlinear surface-enhanced vibrational spectroscopies.

Surface-Enhanced Spectroscopy for Higher-Order Light Scattering: A Combined Experimental and Theoretical Study of Second Hyper-Raman Scattering

Motivated to explore the ultimate limits of surface-enhanced nonlinear spectroscopies, we report on the first observation of molecular second hyper-Raman scattering with the aid of surface enhancement and provide a new theoretical framework for first-principles calculations of the second hyper-Raman effect. Second hyper-Raman enhancement factors, determined to be a minimum of 10(5) times stronger than those in Raman scattering, demonstrate a clear trend toward larger enhancements for nonlinear phenomena, and the nearly quantitative agreement between simulation and experiment provides a unique spectroscopic window into higher-order molecular responses.

Comparison of Property-Oriented Basis Sets for the Computation of Electronic and Nuclear Relaxation Hyperpolarizabilities

In the present work, we perform an assessment of several property-oriented atomic basis sets in computing (hyper)polarizabilities with a focus on the vibrational contributions. Our analysis encompasses the Pol and LPol-ds basis sets of Sadlej and co-workers, the def2-SVPD and def2-TZVPD basis sets of Rappoport and Furche, and the ORP basis set of Baranowska-Łączkowska and Łączkowski. Additionally, we use the d-aug-cc-pVQZ and aug-cc-pVTZ basis sets of Dunning and co-workers to determine the reference estimates of the investigated electric properties for small- and medium-sized molecules, respectively. We combine these basis sets with ab initio post-Hartree-Fock quantum-chemistry approaches (including the coupled cluster method) to calculate electronic and nuclear relaxation (hyper)polarizabilities of carbon dioxide, formaldehyde, cis-diazene, and a medium-sized Schiff base. The primary finding of our study is that, among all studied property-oriented basis sets, only the def2-TZVPD and ORP basis sets yield nuclear relaxation (hyper)polarizabilities of small molecules with average absolute errors less than 5.5%. A similar accuracy for the nuclear relaxation (hyper)polarizabilites of the studied systems can also be reached using the aug-cc-pVDZ basis set (5.3%), although for more accurate calculations of vibrational contributions, i.e., average absolute errors less than 1%, the aug-cc-pVTZ basis set is recommended. It was also demonstrated that anharmonic contributions to first and second hyperpolarizabilities of a medium-sized Schiff base are particularly difficult to accurately predict at the correlated level using property-oriented basis sets. For instance, the value of the nuclear relaxation first hyperpolarizability computed at the MP2/def2-TZVPD level of theory is roughly 3 times larger than that determined using the aug-cc-pVTZ basis set. We link the failure of the def2-TZVPD basis set with the difficulties in predicting the first-order field-induced coordinates. On the other hand, the aug-cc-pVDZ and ORP basis sets overestimate the property in question only by roughly 30%. In this study, we also propose a low-cost composite treatment of anharmonicity that relies on the combination of two basis sets, i.e., a large-sized basis set is employed to determine lowest-order derivatives with respect to the field-induced coordinates, and a medium-sized basis set is used to compute the higher-order derivatives. The results of calculations performed at the MP2 level of theory demonstrate that this approximate scheme is very successful at predicting nuclear relaxation hyperpolarizabilities.

A theoretical study of sum-frequency generation for chiral solutions near electronic resonance

We present a method of calculating sum-frequency generation (SFG) for chiral solutions near electronic resonance including the vibronic contributions, which give reasonable SFG intensities and show the Franck-Condon progressions for SFG. When studying R-1,1'-bi-2-naphthol (R-BN), we found that the calculated spectrum is in good agreement with the experimental one (Phys. Rev. Lett., 2001, 87, 113001). Then we apply this method to investigate SFG for chiral arabinose solutions. Theoretical results show that it may be difficult to observe the corresponding SFG even when the sum-frequency is exactly in resonance with the low-lying excited electronic states. Furthermore, we discuss the reason why SFG of chiral arabinose solutions is small.

Vibronic-structure tracking: a shortcut for vibrationally resolved UV/Vis-spectra calculations

The vibrational coarse structure and the band shapes of electronic absorption spectra are often dominated by just a few molecular vibrations. By contrast, the simulation of the vibronic structure even in the simplest theoretical models usually requires the calculation of the entire set of normal modes of vibration. Here, we exploit the idea of the mode-tracking protocol [M. Reiher and J. Neugebauer, J. Chem. Phys. 118, 1634 (2003)] in order to directly target and selectively calculate those normal modes which have the largest effect on the vibronic band shape for a certain electronic excitation. This is achieved by defining a criterion for the importance of a normal mode to the vibrational progressions in the absorption band within the so-called "independent mode, displaced harmonic oscillator" (IMDHO) model. We use this approach for a vibronic-structure investigation for several small test molecules as well as for a comparison of the vibronic absorption spectra of a truncated chlorophyll a model and the full chlorophyll a molecule. We show that the method allows to go beyond the often-used strategy to simulate absorption spectra based on broadened vertical excitation peaks with just a minimum of computational effort, which in case of chlorophyll a corresponds to about 10% of the cost for a full simulation within the IMDHO approach.

Disentangling vibronic and solvent broadening effects in the absorption spectra of coumarin derivatives for dye sensitized solar cells

Individuation of vibronic and solvent contributions to the spectra of a family of coumarin dyes helps to understand the main differences in their lineshapes.

Theoretical study of the resonance Raman spectra for meso-tetrakis(3,5-di-tertiarybutylphenyl)-porphyrin

Applying time-dependent density functional theory (TDDFT), we study the resonance Raman spectra for the Q and B bands of the meso-tetrakis(3,5-di-tertiarybutylphenyl)-porphyrin (H2TBPP) molecule including both Raman A term (Franck-Condon term) and Raman B term (Herzberg-Teller term) contributions. It is found that Raman B term can be one order of magnitude larger than Raman A term and dominates resonance Raman for the Q band resonance. In comparison with the recent experimental Raman spectra of H2TBPP with incident light frequency 532nm, we predict the absence of 1580cm(-1) band in the resonance Raman spectra which agrees well with the experimental results, whereas the previous theoretical calculation using non-resonance strategy failed to do so.

Assessment of mode-mixing and Herzberg-Teller effects on two-photon absorption and resonance hyper-Raman spectra from a time-dependent approach

A time-dependent approach is presented to simulate the two-photon absorption (TPA) and resonance hyper-Raman scattering (RHRS) spectra including Duschinsky rotation (mode-mixing) and Herzberg-Teller (HT) vibronic coupling effects. The computational obstacles for the excited-state geometries, vibrational frequencies, and nuclear derivatives of transition dipole moments, which enter the expressions of TPA and RHRS cross sections, are further overcome by the recently developed analytical excited-state energy derivative approaches in the framework of time-dependent density functional theory. The excited-state potential curvatures are evaluated at different levels of approximation to inspect the effects of frequency differences, mode-mixing and HT on TPA and RHRS spectra. Two types of molecules, one with high symmetry (formaldehyde, p-difluorobenzene, and benzotrifluoride) and the other with non-centrosymmetry (cis-hydroxybenzylidene-2,3-dimethylimidazolinone in the deprotonated anion state (HDBI(-))), are used as test systems. The calculated results reveal that it is crucial to adopt the exact excited-state potential curvatures in the calculations of TPA and RHRS spectra even for the high-symmetric molecules, and that the vertical gradient approximation leads to a large deviation. Furthermore, it is found that the HT contribution is evident in the TPA and RHRS spectra of HDBI(-) although its one- and two-photon transitions are strongly allowed, and its effect results in an obvious blueshift of the TPA maximum with respect to the one-photon absorption maximum. With the HT and solvent effects getting involved, the simulated blueshift of 1291 cm(-1) agrees well with the experimental measurement.