Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation

In this Letter, we present a pioneering analysis of the density functional approximations (DFAs) beyond the generalized gradient approximation (GGA) for predicting two-photon absorption (2PA) strengths of a set of push-pull π-conjugated molecules. In more detail, we have employed a variety of meta-generalized gradient approximation (meta-GGA) functionals, including SCAN, MN15, and M06-2X, to assess their accuracy in describing the 2PA properties of a chosen set of 48 organic molecules. Analytic quadratic response theory is employed for these functionals, and their performance is compared against the previously studied DFAs and reference data obtained at the coupled-cluster CC2 level combined with the resolution-of-identity approximation (RI-CC2). A detailed analysis of the meta-GGA functional performance is provided, demonstrating that they improve upon their predecessors in capturing the key electronic features of the π-conjugated two-photon absorbers. In particular, the Minnesota functional MN15 shows very promising results as it delivers pleasingly accurate chemical rankings for two-photon transition strengths and excited-state dipole moments.

BF2-Functionalized Benzothiazole Amyloid Markers: Effect of Donor Substituents on One- and Two-Photon Properties

Investigation of amyloids with the aid of fluorescence microscopy provides crucial insights into the development of numerous diseases associated with the formation of aggregates. Here, we present a series of BF2-functionalized benzothiazoles with electron-donating methoxy group(s), which are tested as amyloid fluorescent markers. We evaluate how the position of donor functional group(s) influences optical properties (fluorescence lifetime (τ) and fluorescence quantum yield (FQY)) in a solution and upon binding to amyloids. We elucidate the importance of surrounding environmental factors (hydrogen-bonding network, polarity, and viscosity) on the observed changes in FQY and evaluate how the localization of a donor influences radiative and nonradiative decay pathways. We conclude that a donor attached to the benzothiazole ring contributes to the increment of radiative decay pathways upon binding to amyloids (kr), while the donor attached to the flexible part of a molecule (with rotational freedom) contributes to a decrease in nonradiative decay pathways (knr). We find that the donor-acceptor-donor architecture allows us to obtain 58 times higher FQY of the dye upon binding to bovine insulin amyloids. Finally, we measure two-photon absorption (2PA) cross sections (σ2) of the dyes and their change upon binding by the two-photon excited fluorescence (2PEF) technique. Measurements reveal that dyes that exhibit the increase/decrease of σ2 values when transferred from highly polar solvents to CHCl3 present a similar behavior upon amyloid binding. Our 2PA experimental values are supported by quantum mechanics/molecular mechanics (QM/MM) simulations. Despite this trend, the values of σ2 are not the same, which points out the importance of two-photon absorption measurements of amyloid-dye complexes in order to understand the performance of 2P probes upon binding.

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.

Chromophore Planarity, -BH Bridge Effect, and Two-Photon Activity: Bi- and Ter-Phenyl Derivatives as a Case Study

In this work, we have employed electronic structure theories to explore the effect of the planarity of the chromophore on the two-photon absorption properties of bi- and ter-phenyl systems. To that end, we have considered 11 bi- and 7 ter-phenyl-based chromophores presenting a donor-π-acceptor architecture. In some cases, the planarity has been enforced by bridging the rings at ortho-positions by -CH2 and/or -BH, -O, -S, and -NH moieties. The results presented herein demonstrate that in bi- and ter-phenyl systems, the planarity achieved via a -CH2 bridge increases the 2PA activity. However, the introduction of a bridge with the -BH moiety perturbs the electronic structure to a large extent, thus diminishing the two-photon transition strength to the lowest electronic excited state. As far as two-photon absorption activity is concerned, this work hints toward avoiding -BH bridge(s) to enforce planarity in bi- and ter-phenyl systems; however, one may use -CH2 bridge(s) to achieve the enhancement of the property in question. All of these conclusions have been supported by in-depth analyses based on generalized few-state models.

Photoswitchable Molecular Units with Tunable Nonlinear Optical Activity: A Theoretical Investigation

The first-, second-, and third-order molecular nonlinear optical properties, including two-photon absorption of a series of derivatives, involving two dithienylethene (DTE) groups connected by several molecular linkers (bis(ethylene-1,2-dithiolato)Ni- (NiBDT), naphthalene, quasilinear oligothiophene chains), are investigated by employing density functional theory (DFT). These properties can be efficiently controlled by DTE switches, in connection with light of appropriate frequency. NiBDT, as a linker, is associated with a greater contrast, in comparison to naphthalene, between the first and second hyperpolarizabilities of the "open-open" and the "closed-closed" isomers. This is explained by invoking the low-lying excited states of NiBDT. It is shown that the second hyperpolarizability can be used as an index, which follows the structural changes induced by photochromism. Assuming a Förster type transfer mechanism, the intramolecular excited-state energy transfer (EET) mechanism is studied. Two important parameters related to this are computed: the electronic coupling (VDA) between the donor and acceptor fragments as well as the overlap between the absorption and emission spectra of the donor and acceptor groups. NiBDT as a linker is associated with a low electronic coupling, VDA, value. We found that VDA is affected by molecular geometry. Our results predict that the linker strongly influences the communication between the open-closed DTE groups. The sensitivity of the molecular nonlinear optical properties could assist with identification of molecular isomers.

Decoding the infrared spectra changes upon formation of molecular complexes: the case of halogen bonding in pyridine⋯perfluorohaloarene complexes

A recently developed computational scheme is employed to interpret changes in the infrared spectra of halogen-bonded systems in terms of intermolecular interaction energy components (electrostatic, exchange, induction, dispersion) taking pyridine⋯perfluorohaloarene complexes as examples. For all complexes, we find a strong linear correlation between the different terms of the interaction-induced changes of the IR band associated with an intermolecular halogen bond stretching mode and the corresponding terms of the interaction energy, which implies that the interaction components play similar roles in both properties. This is not true for other vibrational modes localized in one of the monomers studied here, for which the corresponding interaction-induced changes in IR bands may present a completely different decomposition than the interaction energy.

Difluoroborate-based bichromophores: Symmetry relaxation and two-photon absorption

Given potential applications of multiphoton absorbers, in the present work we have studied the symmetry-relaxation effects in one- and two-photon absorption spectra in two bichromophore systems based on difluoroborate core linked by biphenylene or bianthracene moieties. We have employed a palette of experimental methods (synthesis, one- and two-photon spectroscopy, X-ray crystallography) and state-of-the-art computational methods to shed light on how symmetry relaxation, a result of twisting of building blocks, affects one- and two-photon absorption of the two studied fluorescent dyes. Electronic-structure calculations revealed that the planarity of central biphenyl moiety, as well as deviations from planarity up to 30-40 deg., ensure maximum values of two-photon transition strengths. Perpendicular arrangement of phenylene units in biphenylene moiety leads to 20% drop in the two-photon transition strengths. More detailed studies demonstrated that equilibrium structures of both compounds in chloroform solution show very different values of two-photon absorption cross sections at absorption band maxima, i.e. 224 GM for and 134 GM for biphenyle and bianthracene linkers, respectively. The latter value is in good agreement with experimental value obtained using Z-scan method. The difference in two-photon absorption cross section between both compounds can be rationalized based on equilibrium geometry differences, i.e. interplanar angle is 35 deg and 91 deg in the case of biphenylene and bianthracene moiety, respectively. It is thus not beneficial to introduce conformationally locked central linker based on bianthracene moiety.

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%.

Computational Investigations into Two-Photon Fibril Imaging Using the DANIR-2c Probe

The design of novel fibril imaging molecules for medical diagnosis requires the simultaneous optimization of fibril-specific optical properties and binding specificity toward amyloid fibrils. Because of the possibility to monitor internal organs and deep tissues, the two-photon probes that can absorb in the infrared (IR) and near-IR (NIR) region with a significant two-photon absorption cross section are of immense interest. To contribute to this exploration of chemical compounds suitable for two-photon fibril imaging, we have computationally studied the one- and two-photon properties of a donor-acceptor-substituted DANIR-2c probe, which was used for in vivo detection of β-amyloid deposits using fluorescence spectroscopy. In particular, a multiscale computational approach was employed involving molecular docking, molecular dynamics, hybrid QM/MM molecular dynamics, and coupled-cluster/MM to study the binding of the studied probe to amyloid fibril and its one- and two-photon absorption properties in the fibrillar environment. Multiple binding sites are available for this probe in amyloid fibril, and the one corresponding to the largest binding affinity exhibits also the largest and experimentally meaningful two-photon absorption cross section, thus demonstrating the potential of the studied probe in two-photon microscopy.

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

A new computational tool for interpreting infrared spectra of molecular complexes

The popularity of the Infrared (IR) spectroscopy is due to its high interpretive power. This study presents a new computational tool for analyzing the IR spectra of molecular complexes in...

Hyperpolarizabilities of Push-Pull Chromophores in Solution: Interplay between Electronic and Vibrational Contributions

Contemporary design of new organic non-linear optical (NLO) materials relies to a large extent on the understanding of molecular and electronic structure-property relationships revealed during the years by available computational approaches. The progress in theory-hand-in-hand with experiment-has enabled us to identify and analyze various physical aspects affecting the NLO responses, such as the environmental effects, molecular vibrations, frequency dispersion, and system dynamics. Although it is nowadays possible to reliably address these effects separately, the studies analyzing their mutual interplay are still very limited. Here, we employ density functional theory (DFT) methods in combination with an implicit solvent model to examine the solvent effects on the electronic and harmonic as well as anharmonic vibrational contributions to the static first hyperpolarizability of a series of push-pull α,ω-diphenylpolyene oligomers, which were experimentally shown to exhibit notable second-order NLO responses. We demonstrate that the magnitudes of both vibrational and electronic contributions being comparable in the gas phase significantly increase in solvents, and the enhancement can be, in some cases, as large as three- or even four-fold. The electrical and mechanical anharmonic contributions are not negligible but cancel each other out to a large extent. The computed dynamic solute NLO properties of the studied systems are shown to be in a fair agreement with those derived from experimentally measured electric-field-induced second-harmonic generation (EFISHG) signals. Our results substantiate the necessity to consider concomitantly both solvation and vibrational effects in modeling static NLO properties of solvated systems.

How Reliable Are Modern Density Functional Approximations to Simulate Vibrational Spectroscopies?

We show that properties of molecules with low-frequency modes calculated with density functional approximations (DFAs) suffer from spurious oscillations along the nuclear displacement coordinate due to numerical integration errors. Occasionally, the problem can be alleviated using extensive integration grids that compromise the favorable cost-accuracy ratio of DFAs. Since spurious oscillations are difficult to predict or identify, DFAs are exposed to severe performance errors in IR and Raman intensities and frequencies or vibrational contributions to any molecular property. Using Fourier spectral analysis and digital signal processing techniques, we identify and quantify the error due to these oscillations for 45 widely used DFAs. LC-BLYP and BH&H are revealed as the only functionals showing robustness against the spurious oscillations of various energy, dipole moment, and polarizability derivatives with respect to a nuclear displacement coordinate. Given the ubiquitous nature of molecules with low-frequency modes, we warrant caution in using modern DFAs to simulate vibrational spectroscopies.

First-order hyperpolarizabilities of propellanes: elucidating structure-property relationships

Following recent experimental work demonstrating strong nonlinear optical properties, namely second harmonic generation of light, in crystals composed of 16,20-dinitro-(3,4,8,9)-dibenzo-2,7-dioxa-5,10-diaza[4.4.4]propellane molecules [A. Miniewicz, S. Bartkiewicz, E. Wojaczyńska, T. Galica, R. Zaleśny and R. Jakubas, J. Mater. Chem. C, 2019, 7, 1255-1262] in this paper we aim to investigate "structure-property" relationships for a series of 16 propellanes presenting a wide palette of substituents with varying electron-accepting/donating capabilities. To that end, we use electronic- and vibrational-structure theories and a recently developed generalized few-state model combined with a range-separated CAM-B3LYP functional to analyze electronic and vibrational contributions to the first hyperpolarizability for the whole series of molecules. The variations in computed properties are large among the studied set of substituents and can reach an order of magnitude. It has been demonstrated that the maximum values of frequency-independent first hyperpolarizability are expected for strong electron-accepting NO₂ substituents, but only at the preferred position with respect to the electronegative oxygen atom in the 1,4-oxazine moiety. This holds for electronic as well as vibrational counterparts.

Much of a Muchness: On the Origins of Two- and Three-Photon Absorption Activity of Dipolar Y-Shaped Chromophores

The molecular origin of two- (2PA) and three-photon absorption (3PA) activity in three experimentally studied chromophores, prototypical dipolar systems, is investigated. To that end, a generalized few-state model (GFSM) formula is derived for the 3PA transition strength for nonhermitian theories and employed at the coupled-cluster level of theory. Using various computational techniques such as molecular dynamics, linear and quadratic response theories, and GFSM, an in-depth analysis of various optical channels involved in 2PA and 3PA processes is presented. It is found that the four-state model involving the second and third excited singlet states as intermediates is the smallest model among all considered few-state approximations that produces 2PA and 3PA transition strengths (for S₀ → S₁ transition) close to the reference results. By analyzing various optical channels appearing in these models and involved in studied multiphoton processes, we found that the 2PA and 3PA activities in all the three chromophores are dominated and hence controlled by the dipole moment of the final excited state. The similar origins of the 2PA and the 3PA in these prototypical dipolar chromophores suggest transferability of structure–property relations from the 2PA to the 3PA domain.

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.

Infrared Spectra of Hydrogen-Bonded Molecular Complexes Under Spatial Confinement

Infrared (IR) spectroscopy is commonly used in chemical laboratories to study the geometrical structure of molecules and molecular complexes. The analysis of experimental IR spectra can nowadays be reliably supported by the results of quantum-chemical computations as vibrational frequencies and corresponding vibrational transition intensities are routinely calculated using harmonic approximation by virtually all quantum chemistry packages. In the present study we combine the methodology of computing vibrational spectra using high-level electron correlation treatments with an analytical potential-based approach to take into account spatial confinement effects. Using this approach, we perform a pioneering analysis of the impact of the spatial confinement caused by a cylindrical harmonic oscillator potential on the harmonic vibrational transition intensities and frequencies of two hydrogen-bonded complexes: HCN…HCN and HCN…HNC. The emphasis is put on the largest-intensity bands, which correspond to the stretching vibrations. The obtained results demonstrate that embedding the molecular complexes in an external confining potential causes significant changes of transition intensities and vibrational frequencies.

Substituted 2-(2-hydroxyphenyl)-3H-quinazolin-4-ones and their difluoroboron complexes: Synthesis and photophysical properties

2-(2-Hydroxyphenyl)-3H-quinazolin-4-ones with diverse substituents at phenol ring and their six-membered difluoroboron complexes have been synthesized via few-stage approach. The photophysical properties of target compounds have been investigated in two solvents as well as in the solid state. The nature of substituents and substitution point in the phenol moiety of ligands and resulting BF₂-complexes on the photophysical properties of dyes have been explored. The complex bearing two t-Bu groups proved to be the most emissive in solid state, whereas its 5-methoxy and 4-diethylamino counterparts possess strong emission in toluene solution. The dyes exhibited large Stokes shifts which was attributed to excited state intramolecular proton transfer (ESIPT). Additionally, fluorescence of quinazolinones in the mixture of THF/water was studied. All ligands demonstrated emission enhancement with increase of water fraction which was due to aggregation induced emission.

Two-Photon Absorption Activity of BOPHY Derivatives: Insights from Theory

We present a theoretical study of a two-photon absorption (2PA) process in dipolar and quadrupolar systems containing two BF₂ units. For this purpose, we considered 13 systems studied by Ponce-Vargas et al. [J. Phys. Chem. B2017, 121, 10850−1085829136383] and performed linear and quadratic response theory calculations based on the RI-CC2 method to obtain the 2PA parameters. Furthermore, using the recently developed generalized few-state model, we provided an in-depth view of the changes in 2PA properties in the molecules considered. Our results clearly indicate that suitable electron-donating group substitution to the core BF₂ units results in a large red-shift of the two-photon absorption wavelength, thereby entering into the desired biological window. Furthermore, the corresponding 2PA strength also increases significantly (up to 30-fold). This makes the substituted systems a potential candidate for biological imaging.

Multiscale Modeling of Two-Photon Probes for Parkinson's Diagnostics Based on Monoamine Oxidase B Biomarker

Monoamine oxidase B (MAO-B) is a potential biomarker for Parkinson's disease (PD), a neurodegenerative disease associated with the loss of motor activities in human subjects. The disease state is associated with dopamine deprival, and so the inhibitors of MAO-B can serve as therapeutic drugs for PD. Since the expression level of MAO-B directly correlates to the disease progress, the distribution and population of this enzyme can be employed to monitor disease development. One of the approaches available for estimating the population is two-photon imaging. The ligands used for two-photon imaging should have high binding affinity and binding specificity toward MAO-B along with significant two-photon absorption cross sections when they are bound to the target. In this article, we study using a multiscale modeling approach, the binding affinity and spectroscopic properties (one- and two-photon absorption) of three (Flu1, Flu2, Flu3) of the currently available probes for monitoring the MAO-B level. We report that the binding affinity of the probes can be explained using the molecular size and binding cavity volume. The experimentally determined one-photon absorption spectrum is well reproduced by the employed QM/MM approaches, and the most accurate spectral shifts, on passing from one probe to another, are obtained at the coupled-cluster (CC2) level of theory. An important conclusion from this study is also the demonstration that intrinsic molecular two-photon absorption strengths (δ^2PA) increase in the order δ^2PA (Flu1) > δ^2PA (Flu2) > δ^2PA (Flu3). This is in contrast with experimental data, which predict similar values of two-photon absorption cross sections for Flu1 and Flu3. We demontrate, based on the results of electronic-structure calculations for Flu1 that this discrepancy cannot be explained by an explicit account for neighboring residues (which could lead to charge transfer between a probe and neighboring aromatic amino acids thus boosting δ^2PA). In summary, we show that the employed multiscale approach not only can optimize two-photon absorption properties and verify binding affinity, but it can also help in detailed analyses of experimental data.

Controlling Two-Photon Action Cross Section by Changing a Single Heteroatom Position in Fluorescent Dyes

The optimization of nonlinear optical properties for "real-life" applications remains a key challenge for both experimental and theoretical approaches. In particular, for two-photon processes, maximizing the two-photon action cross section (TPACS), the figure of merit for two-photon bioimaging spectroscopy, requires simultaneously controlling all its components. In the present Letter, a series of difluoroborates presenting various heterocyclic rings as an electron acceptor have been synthesized and their absorption, fluorescence, photoisomerization, and two-photon absorption features have been analyzed using both experimental and theoretical approaches. Our results demonstrate that the TPACS values can be fine-tuned by changing the position of a single heteroatom, which alters the fluorescence quantum yields without changing the intrinsic two-photon absorption cross section. This approach offers a new strategy for optimizing TPACS.

Predictions of High-Order Electric Properties of Molecules: Can We Benefit from Machine Learning?

There is an exigency of adopting machine learning techniques to screen and discover new materials which could address many societal and technological challenges. In this work, we follow this trend and employ machine learning to study (high-order) electric properties of organic compounds. The results of quantum-chemistry calculations of polarizability and first hyperpolarizability, obtained for more than 50,000 compounds, served as targets for machine learning-based predictions. The studied set of molecular structures encompasses organic push-pull molecules with variable linker lengths. Moreover, the diversified set of linkers, composed of alternating single/double and single/triple carbon-carbon bonds, was considered. This study demonstrates that the applied machine learning strategy allows us to obtain the correlation coefficients, between predicted and reference values of (hyper)polarizabilities, exceeding 0.9 on training, validation, and test set. However, in order to achieve such satisfactory predictive power, one needs to choose the training set appropriately, as the machine learning methods are very sensitive to the linker-type diversity in the training set, yielding catastrophic predictions in certain cases. Furthermore, the dependence of (hyper)polarizability on the length of spacers was studied in detail, allowing for explanation of the appreciably high accuracy of employed approaches.

Partitioning of interaction-induced nonlinear optical properties of molecular complexes. II. Halogen-bonded systems

Following our study on hydrogen-bonded (HB) complexes [Phys. Chem. Chem. Phys., 2018, 20, 19841], the physical nature of interaction-induced (non)linear optical properties of another important class of molecular complexes, namely halogen-bonded (XB) systems, was analyzed in this study. The excess electronic and nuclear relaxation (hyper)polarizabilities of nine representative XB complexes covering a wide range of halogen-bond strengths were computed. The partitioning of the excess properties into individual interaction-energy components (electrostatic, exchange, induction, dispersion) was performed by using the variational-perturbational energy decomposition scheme at the MP2/aug-cc-pVTZ level of theory and further supported by calculations with the SCS-MP2 method. In the case of the electronic interaction-induced properties, the physical composition of Δαel and Δγel was found to be very similar for the two types of bonding, despite the different nature of the binding. For Δβel, the XB complexes exhibit a more systematic interplay of interaction-energy contributions compared to the HB systems studied in the previous work. Our analysis revealed that the patterns of interaction-energy contributions to the interaction-induced nuclear-relaxation contributions to the linear polarizability and the first hyperpolarizability are very similar. For both properties the exchange repulsion term is canceled out by the electrostatic and delocalization terms. The physical composition of these contributions is analogous to those observed for the HB complexes.

Can Density Functional Theory Be Trusted for High-Order Electric Properties? The Case of Hydrogen-Bonded Complexes

This work reports on an extensive assessment of the performance of a wide palette of density functional approximations in predicting the (high-order) electric properties of hydrogen-bonded complexes. To this end, we compute the electronic and vibrational contributions to the electric polarizability and the first and second hyperpolarizabilities, using the CCSD(T)/aug-cc-pVTZ level of theory as reference. For all the studied properties, the average absolute errors below 20% can only be obtained using the CAM-B3LYP functional, while LC-BLYP and MN15 are shown to be only slightly less accurate (average absolute errors not exceeding 30%). Among Minnesota density functionals, i.e., M06, M06-2X, and MN15, we only recommend the latter one, which quite accurately predicts the electronic and vibrational (hyper)polarizabilities. We also analyze the optimal tuning of the range-separation parameter μ for the LC-BLYP functional, finding that this approach does not bring any systematic improvement in the predictions of electronic and vibrational (hyper)polarizabilities and the accuracy of computed properties is largely system-dependent. Finally, we report huge errors in predicting the vibrational second hyperpolarizability by ωB97X, M06, and M06-2X functionals. Based on the explicit evaluation of anharmonic terms contributing to the second hyperpolarizability, this failure is traced down to a poor determination of third- and fourth-order energy derivatives with respect to normal modes. These results reveal serious flaws of some density functional approximations and suggest caution in selecting the appropriate functional to calculate not only electronic and vibrational (hyper)polarizabilities but also other molecular properties that contain vibrational anharmonic contributions.

Two-photon absorption of BF2-carrying compounds: insights from theory and experiment

This communication presents a structure-property study of a few novel pyridine-based difluoroborate compounds with a N-BF₂-O core, which exhibit outstanding fluorescence properties. To exploit their potential for two-photon bioimaging, relationships between the two-photon action cross section and systematic structural modifications have been investigated and unravelled.

Unusual binding-site-specific photophysical properties of a benzothiazole-based optical probe in amyloid beta fibrils

Varying electronic structure of BTA-3 probe in different binding sites in amyloid fibrils is the key mechanism behind its site-specific photophysical properties.

Partitioning of interaction-induced nonlinear optical properties of molecular complexes. I. Hydrogen-bonded systems

Interaction-induced electronic and vibrational (hyper)polarizabilities were decomposed into different interaction types (electrostatic, exchange, induction and dispersion).

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.

Vibrational nonlinear optical properties of spatially confined weakly bound complexes

This study focuses on the theoretical description of the influence of spatial confinement on the electronic and vibrational contributions to (hyper)polarizabilities of two dimeric hydrogen bonded systems, namely HCNHCN and HCNHNC. A two-dimensional analytical potential is employed to render the confining environment (e.g. carbon nanotube). Based on the results of the state-of-the-art calculations, performed at the CCSD(T)/aug-cc-pVTZ level of theory, we established that: (i) the influence of spatial confinement increases with increasing order of the electrical properties, (ii) the effect of spatial confinement is much larger in the case of the electronic than vibrational contribution (this holds for each order of the electrical properties) and (iii) the decrease in the static nuclear relaxation first hyperpolarizability upon the increase of confinement strength is mainly due to changes in the harmonic term, however, in the case of nuclear relaxation second hyperpolarizability the anharmonic terms contribute more to the drop of this property.

Two-photon absorption of the spatially confined LiH molecule

In the present contribution we study the influence of spatial restriction on the two-photon dipole transitions between the X¹Σ⁺ and A¹Σ⁺ states of lithium hydride. The bond-length dependence of the two-photon absorption strength is also analyzed for the first time in the literature. The highly accurate multiconfiguration self-consistent field (MCSCF) method and response theory are used to characterize the electronic structure of the studied molecule. In order to render the effect of orbital compression we apply a two-dimensional harmonic oscillator potential, mimicking the topology of cylindrical confining environments (e.g. carbon nanotubes, quantum wires). Among others, the obtained results provide evidence that at large internuclear distances the TPA response of lithium hydride may be significantly enhanced and this effect is much more pronounced upon embedding of the LiH molecule in an external confining potential. To understand the origin of the observed variation in the two-photon absorption response a two-level approximation is employed.

Elucidating the Mechanism of Zn(2+) Sensing by a Bipyridine Probe Based on Two-Photon Absorption

In this work, we examine, by means of computational methods, the mechanism of Zn(2+) sensing by a bipyridine-centered, D-π-A-π-D-type ratiometric molecular probe. According to recently published experimental data [Divya, K. P.; Sreejith, S.; Ashokkumar, P.; Yuzhan, K.; Peng, Q.; Maji, S. K.; Tong, Y.; Yu, H.; Zhao, Y.; Ramamurthy, P.; Ajayaghosh, A. A ratiometric fluorescent molecular probe with enhanced two-photon response upon Zn(2+) binding for in vitro and in vivo bioimaging. Chem. Sci. 2014, 5, 3469-3474], after coordination to zinc ions the probe exhibits a large enhancement of the two-photon absorption cross section. The goal of our investigation was to elucidate the mechanism behind this phenomenon. For this purpose, linear and nonlinear optical properties of the unbound (cation-free) and bound probe were calculated, including the influence of solute-solvent interactions, implicitly using a polarizable continuum model and explicitely employing the QM/MM approach. Because the results of the calculations indicate that many conformers of the probe are energetically accessible at room temperature in solution and hence contribute to the signal, structure-property relationships were also taken into account. Results of our simulations demonstrate that the one-photon absorption bands for both the unbound and bound forms correspond to the bright π → π* transition to the first excited state, which, on the other hand, exhibits negligible two-photon activity. On the basis of the results of the quadratic response calculations, we put forward a notion that it is the second excited state that gives the strong signal in the experimental nonlinear spectrum. To explain the differences in the two-photon absorption activity for the two lowest-lying excited states and nonlinear response enhancement upon binding, we employed the generalized few-state model including the ground, first, and second excited states. The analysis of the optical channel suggests that the large two-photon response is due to the coordination-induced increase of the transition moment from the first to the second excited state.

On the physical origins of interaction-induced vibrational (hyper)polarizabilities

This paper presents the results of a pioneering exploration of the physical origins of vibrational contributions to the interaction-induced electric properties of molecular complexes. In order to analyze the excess nuclear relaxation (hyper)polarizabilities, a new scheme was proposed which relies on the computationally efficient Bishop-Hasan-Kirtman method for determining the nuclear relaxation contributions to electric properties. The extension presented herein is general and can be used with any interaction-energy partitioning method. As an example, in this study we employed the variational-perturbational interaction-energy decomposition scheme (at the MP2/aug-cc-pVQZ level) and the extended transition state method by employing three exchange-correlation functionals (BLYP, LC-BLYP, and LC-BLYP-dDsC) to study the excess properties of the HCN dimer. It was observed that the first-order electrostatic contribution to the excess nuclear relaxation polarizability cancels with the negative exchange repulsion term out to a large extent, resulting in a positive value of Δα(nr) due to the contributions from the delocalization and the dispersion terms. In the case of the excess nuclear relaxation first hyperpolarizability, the pattern of interaction contributions is very similar to that for Δα(nr), both in terms of their sign as well as relative magnitude. Finally, our results show that the LC-BLYP and LC-BLYP-dDsC functionals, which yield smaller values of the orbital relaxation term than BLYP, are more successful in predicting excess properties.

Application of spectroscopic and theoretical methods in the studies of photoisomerization and photophysical properties of the push-pull styryl-benzimidazole dyes

The synthesis and spectroscopic properties of a series of substituted 1,3-dimethyl-2-aminostyrylbenzimidazolium iodides are described and discussed. The products were identified by NMR, IR and UV-Vis spectroscopy and elemental analysis. Their electronic absorption and fluorescence band positions are affected by the character of the substituent and by the solvent polarity. The fluorescence decay of the dyes shows two lifetimes interpreted in terms of emission from two forms of the dye in the excited state. Moreover, the photochemical trans→cis isomerization is reported for these compounds. It occurs from the first excited singlet state of the trans isomer to the cis isomer following a trans-S0→ S1 excitation. The electron-donating character of the substituent in a styrene moiety is one of the crucial factors influencing the photoisomerization process. The structure of the cis isomer was established by (1)H and (15)N NMR. Experimental studies are supported by the results of quantum chemical calculations.

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.

Relation between Nonlinear Optical Properties of Push-Pull Molecules and Metric of Charge Transfer Excitations

We establish the relationships between the metric of charge transfer excitation (Δr) for the bright ππ* state and the two-photon absorption probability as well as the first hyperpolarizability for two families of push-pull π-conjugated systems. As previously demonstrated by Guido et al. (J. Chem. Theory Comput. 2013, 9, 3118-3126), Δr is a measure for the average hole-electron distance upon excitation and can be used to discriminate between short- and long-range electronic excitations. We indicate two new benefits from using this metric for the analyses of nonlinear optical properties of push-pull systems. First, the two-photon absorption probability and the first hyperpolarizability are found to be interrelated through Δr; if β ∼ (Δr)(k), then roughly, δ(TPA) ∼ (Δr)(k+1). Second, a simple power relation between Δr and the molecular hyperpolarizabilities of push-pull systems offers the possibility of estimating properties for longer molecular chains without performing calculations of high-order response functions explicitly. We further demonstrate how to link the hyperpolarizabilities with the chain length of the push-pull π-conjugated systems through the metric of charge transfer.

One- and two-photon absorption of a spiropyran-merocyanine system: experimental and theoretical studies

We report on the nonlinear optical properties measurements and quantum-chemical calculations of a well-known photochromic system consisting of spiropyran and the merocyanine photoproduct. The study of nonlinear absorption and refraction properties of the molecules dissolved in chloroform were performed with the Z-scan technique, using femtosecond pulses in a wide range of wavelengths. Maxima in the two-photon absorption spectrum at 700 and 1050 nm were found for the merocyanine form, and the corresponding two-photon absorption cross section is 80 GM and 20 GM, respectively. The latter feature does not vanish completely in the nonlinear spectrum of the spiropyran form, possibly because of the existence of some photoconversion caused by the laser beam during the measurements. A nonlinear absorption peak at 900 nm is found in the spiropyran form with an effective cross section of about 20 GM; it is likely due to three-photon absorption or to absorption by some intermediate species. The experimental data are supported by calculations performed with the use of a hybrid quantum mechanics-molecular mechanics approach.