TDDFT Investigation of the Raman and Resonant Raman Spectra of Fluorescent Protein Chromophore Models

The off-resonance and resonant Raman spectra have been simulated for models of fluorescent protein chromophores, those of the green fluorescent protein (GFP, called FP1) and of DsRed (called FP2), which presents a longer π-conjugated path, with the aim of providing a systematic investigation of structural but also computational aspects. These were performed at the (time-dependent) density functional theory [(TD)DFT] level. The off-resonance intensities have been calculated from the derivatives of the frequency-dependent polarizability with respect to the normal coordinates while the resonant ones have been evaluated using Huang-Rhys factors determined from the gradients of the excitation energies with respect to the normal coordinates. When applied with the M05 meta-GGA exchange-correlation functional, this simple computational scheme can reproduce most of the experimental Raman signatures of FP1 in its protonated and deprotonated forms, the differences of vibrational signatures of the cis (Z) and trans (E) isomers, as well as their changes as a function of the excitation wavelength. On the other hand, testing the predictions made for FP2 would require new experimental work. It was also observed that simulations with methods that inadequately predict the resonant Raman spectra could nevertheless produce a UV-vis absorption spectrum that is quite similar to the one obtained with better methods, once realistic peak broadening has been applied.

Second-Order Nonlinear Optics Response of the Boron-Dipyrromethenes-Based Mislinked Expanded Porphyrins: Revealing the Role of the -BF2 Group

Here, the mislinked expanded porphyrins singly (labeled A) and doubly (labeled B) neo-confused [22]smaragdyrin, the boron-dipyrromethenes-based mislinked expanded porphyrins singly (labeled C) and doubly (labeled D) neo-confused [22]smaragdyrin, where both C and D include a -BF₂ group, are chosen to serve as the study objects, and theoretical calculations are carried out to study the role of the -BF₂ group in the second-order nonlinear optics (NLO) behaviors. Results highlighted that the -BF₂ group plays an important role for the second-order behaviors in mislinked expanded porphyrins; namely, embedding the -BF₂ group well enhanced the hyper-Rayleigh scattering (HRS) value {β_HRS(0;0,0)}, C{βHRS(0;0,0)}A{βHRS(0;0,0)} = 2.0 and D{βHRS(0;0,0)}B{βHRS(0;0,0)} = 2.9, main owning to the fact that installing -BF₂ increases the electron delocalization degree and decreases the excited energy of the crucial excited state.

All-Atom Quantum Mechanical Calculation of the Second-Harmonic Generation of Fluorescent Proteins

Fluorescent proteins (FPs) are biotags of choice for second-harmonic imaging microscopy (SHIM). Because of their large size, computing their second-harmonic generation (SHG) response represents a great challenge for quantum chemistry. In this contribution, we propose a new all-atom quantum mechanics methodology to compute SHG of large systems. This is now possible because of two recent implementations: the tight-binding GFN2-xTB method to optimize geometries and a related version of the simplified time-dependent density functional theory (sTD-DFT-xTB) to evaluate quadratic response functions. In addition, a new dual-threshold configuration selection scheme is introduced to reduce the computational costs while retaining overall similar accuracy. This methodology was tested to evaluate the SHG of the proteins iLOV and bacteriorhodopsin (bR). In the case of bR, quantitative agreement with respect to experiment was reached for the out-of-resonance low-energy part of the β_HRS frequency dispersion. This work paves the way toward an accurate prediction of the SHG of large structures-a requirement for the design of new and improved SHIM biotags.

Harmonic Generation Microscopy 2.0: New Tricks Empowering Intravital Imaging for Neuroscience

Optical harmonic generation, e.g., second- (SHG) and third-harmonic generation (THG), provides intrinsic contrasts for three-dimensional intravital microscopy. Contrary to two-photon excited fluorescence (TPEF), however, they have found relatively specialized applications, such as imaging collagenous and non-specific tissues, respectively. Here we review recent advances that broaden the capacity of SHG and THG for imaging the central nervous system in particular. The fundamental contrast mechanisms are reviewed as they encode novel information including molecular origin, spectroscopy, functional probes, and image analysis, which lay foundations for promising future applications in neuroscience.

Nonlinear-response properties in a simplified time-dependent density functional theory (sTD-DFT) framework: Evaluation of the first hyperpolarizability

Recent developments in nonlinear imaging microscopy show the need to implement new theoretical tools, which are able to characterize nonlinear optical properties in an efficient way. For second-harmonic imaging microscopy (SHIM), quantum chemistry could play an important role to design new exogenous dyes with enhanced first hyperpolarizabilities or to characterize the response origin in large endogenous biological systems. Such methods should be able to screen a large number of compounds while reproducing their trends and to treat large systems in reasonable computation times. To fulfill these requirements, we present a new simplified time-dependent density functional theory (sTD-DFT) implementation to evaluate the first hyperpolarizability where the Coulomb and exchange integrals are approximated by short-range damped Coulomb interactions of transition density monopoles. For an ultra-fast computation of the first hyperpolarizability, a tight-binding version (sTD-DFT-xTB) is also proposed. In our implementation, a sTD-DFT calculation is more than 600 time faster with respect to a regular TD-DFT treatment, while the xTB version speeds up the entire calculation further by at least two orders of magnitude. We challenge our implementation on three test cases: typical push-pull π-conjugated compounds, fluorescent proteins, and a collagen model, which were selected to model requirements for SHIM applications.

Long- and Short-Range Electrostatic Fields in GFP Mutants: Implications for Spectral Tuning

The majority of protein functions are governed by their internal local electrostatics. Quantitative information about these interactions can shed light on how proteins work and allow for improving/altering their performance. Green fluorescent protein (GFP) and its mutation variants provide unique optical windows for interrogation of internal electric fields, thanks to the intrinsic fluorophore group formed inside them. Here we use an all-optical method, based on the independent measurements of transition frequency and one- and two-photon absorption cross sections in a number of GFP mutants to evaluate these internal electric fields. Two physical models based on the quadratic Stark effect, either with or without taking into account structural (bond-length) changes of the chromophore in varying field, allow us to separately evaluate the long-range and the total effective (short- and long-range) fields. Both types of the field quantitatively agree with the results of independent molecular dynamic simulations, justifying our method of measurement.

Organized chromophoric assemblies for nonlinear optical materials: towards (sub)wavelength scale architectures

Photonic circuits are expected to greatly contribute to the next generation of integrated chips, as electronic integrated circuits become confronted with bottlenecks such as heat generation and bandwidth limitations. One of the main challenges for the state-of-the-art photonic circuits lies in the development of optical materials with high nonlinear optical (NLO) susceptibilities, in particular in the wavelength and subwavelength dimensions which are compatible with on-chip technologies. In this review, the varied approaches to micro-/nanosized NLO materials based on building blocks of bio- and biomimetic molecules, as well as synthetic D-π-A chromophores, have been categorized as supramolecular self-assemblies, molecular scaffolds, and external force directed assemblies. Such molecular and supramolecular NLO materials have intrinsic advantages, such as structural diversities, high NLO susceptibilities, and clear structure-property relationships. These "bottom-up" fabrication approaches are proposed to be combined with the "top-down" techniques such as lithography, etc., to generate multifunctionality by coupling light and matter on the (sub)wavelength scale.

N-Methylbenzoaza-18-crown-6-ether derivatives as efficient alkali metal cations sensors: the dipole moment and first hyperpolarizability

1-Li+, 1-Na+ and 1-K+ complexes formed by N-methylbenzoaza-18-crown-6-ether derivatives with one alkali metal cation were investigated. Their dipole moments and first hyperpolarizabilities take on opposite trends with increasing the atomic number.

SECOND-HARMONIC GENERATION OF FLUORESCENT PROTEINS

We theoretically study the second-order nonlinear optical properties of six fluorescent proteins (FPs), such as green fluorescent protein (GFP), BFP, enhanced BFP (eBFP), CFP, YFP, and DsRed. To begin with, the geometries of all these FP chromophores are optimized at B3LYP/6-311++G** level in a water medium and the polarized continuum model (PCM in water) method is adopted. Using a time-dependent density functional theory (TDDFT) method, the electronic structures and excited-state properties of chromophores are determined. Here we employ TDDFT combining with the sum-over-states (SOS) method to calculate the first-order hyperpolarizability for second-harmonic generation (SHG) optical process. Moreover, we discuss the origin of the nonlinear optical response and determine what caused the variation of first-order hyperpolarizability. Our calculations show that the charge transfers of π → π* in the central conjugated structure and p → π* charge transfers from the side chain R1 to conjugated structure of chromophores markedly affect the first-order hyperpolarizability.

Improving the second-order nonlinear optical response of fluorescent proteins: the symmetry argument

We have successfully designed and expressed a new fluorescent protein with improved second-order nonlinear optical properties. It is the first time that a fluorescent protein has been rationally altered for this particular characteristic. On the basis of the specific noncentrosymmetry requirements for second-order nonlinear optical effects, we had hypothesized that the surprisingly low first hyperpolarizability (β) of the enhanced yellow fluorescent protein (eYFP) could be explained by centrosymmetric stacking of the chromophoric Tyr66 and the neighboring Tyr203 residue. The inversion center was removed by mutating Tyr203 into Phe203, with minor changes in the linear optical properties and even an improved fluorescence quantum yield. Structure determination by X-ray crystallography as well as linear optical characterization corroborate a correct folding and maturation. Measurement of β by means of hyper-Rayleigh scattering (HRS) as well as their analysis using quantum chemistry calculations validate our hypothesis. This observation can eventually lead to improved red fluorescent proteins for even better performance. On the basis of the specific function (second-harmonic generation), the color of its emission, and in analogy with the "fruit" names, we propose SHardonnay as the name for this Tyr203Phe mutant of eYFP.

Practical Model for First Hyperpolarizability Dispersion Accounting for Both Homogeneous and Inhomogeneous Broadening Effects

A practical yet accurate dispersion model for the molecular first hyperpolarizability β is presented, incorporating both homogeneous and inhomogeneous line broadening because these affect the β dispersion differently, even if they are indistinguishable in linear absorption. Consequently, combining the absorption spectrum with one free shape-determining parameter Ginhom, the inhomogeneous line width, turns out to be necessary and sufficient to obtain a reliable description of the β dispersion, requiring no information on the homogeneous (including vibronic) and inhomogeneous line broadening mechanisms involved, providing an ideal model for practical use in extrapolating experimental nonlinear optical (NLO) data. The model is applied to the efficient NLO chromophore picolinium quinodimethane, yielding an excellent fit of the two-photon resonant wavelength-dependent data and a dependable static value β0 = 316 × 10(-30) esu. Furthermore, we show that including a second electronic excited state in the model does yield an improved description of the NLO data at shorter wavelengths but has only limited influence on β0.