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

The eXact integral simplified time-dependent density functional theory (XsTD-DFT)

In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14 eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.

Charge Regulation at the Nanoscale as Evidenced from Light-Responsive Nanoemulsions

Emulsions are indispensable in everyday life, and the demand for emulsions' diversity and control of properties is therefore substantial. As emulsions possess a high internal surface area, an understanding of the oil/water (o/w) interfaces at the molecular level is fundamental but often impaired by experimental limitations to probe emulsion interfaces in situ. Here, we have used light-responsive surfactants (butyl-AAP) that can photoisomerize between E and Z isomers by visible and UV light irradiation to tune the emulsion interfaces. This causes massive changes in the interface tension at the extended o/w interfaces in macroemulsions and a drastic shift in the surfactants' critical micelle concentration, which we show can be used to control both the stability and phase separation. Strikingly different from macroemulsions are nanoemulsions (RH ∼90 nm) as these are not susceptible to E/Z photoisomerization of the surfactants in terms of changes in their droplet size or ζ-potential. However, in situ second-harmonic scattering and pulsed-field gradient nuclear magnetic resonance (NMR) experiments show dramatic and reversible changes in the surface excess of surfactants at the nanoscopic interfaces. The apparent differences in ζ-potentials and surface excess provide evidence for a fixed charge to particle size ratio and the need for counterion condensation to renormalize the particle charge to a critical charge, which is markedly different compared to the behavior of very large particles in macroemulsions. Thus, our findings may have broader implications as the electrostatic stabilization of nanoparticles requires much lower surfactant concentrations, allowing for a more sustainable use of surfactants.

Ultrafast Evaluation of Two-Photon Absorption with Simplified Time-Dependent Density Functional Theory

This work presents the theoretical background to evaluate two-photon absorption (2PA) cross-sections in the framework of simplified time-dependent density functional theory (sTD-DFT). Our new implementation allows the ultrafast evaluation of 2PA cross-sections for large molecules based on a regular DFT ground-state determinant as well as a variant employing our tight-binding sTD-DFT-xTX flavor for very large systems. The method is benchmarked against higher-level calculations for trans-stilbene and typical fluorescent protein chromophores. For eGFP, a quadrupolar chromophore and its branched version, the flavine mono-nucleotide, and the iLOV protein, we compare sTD-DFT 2PA spectra to experimental ones. This includes extension and testing of our all-atom quantum chemistry methodology for the evaluation of 2PA for a system of ∼2000 atoms, providing striking agreement with the experimental spectrum.

Evaluating fast methods for static polarizabilities on extended conjugated oligomers

Given the importance of accurate polarizability calculations to many chemical applications, coupled with the need for efficiency when calculating the properties of sets of molecules or large oligomers, we present a benchmark study examining possible calculation methods for polarizable materials. We first investigate the accuracy of the additive model used in GFN2, a highly-efficient semi-empirical tight-binding method, and the D4 dispersion model, comparing its predicted additive polarizabilities to ωB97XD results for a subset of PubChemQC and a compiled benchmark set of molecules spanning polarizabilities from approximately 3 ų to 600 ų, with some compounds in the range of approximately 1200-1400 ų. Although we find additive GFN2 polarizabilities, and thus D4, to have large errors with polarizability calculations on large conjugated oligomers, it would appear an empirical quadratic correction can largely remedy this. We also compare the accuracy of DFT polarizability calculations run using basis sets of varying size and level of augmentation, determining that a non-augmented basis set may be used for large, highly polarizable species in conjunction with a linear correction factor to achieve accuracy extremely close to that of aug-cc-pVTZ.

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.

New structural insights into the stability of Au22(SR)16 nanocluster under ring model guidance

This study presents thorough structural insights into the stability of crystallized Au₂₂(SAdm)₁₆ (HSAdm = 1-adamantanethiol) nanocluster. With the recently developed Ring Model for describing the interaction between inner gold cores and outer protecting ligands in thiolate-protected gold nanoclusters, the experimental spontaneous transformation from the crystallized Au₂₂(SAdm)₁₆ to Au₂₁(SAdm)₁₅ could be well understood as structurally unfavorable for the current Au₂₂(SAdm)₁₆ and could also be attributed to the weaker aurophilic interaction between the inner Au₄ core and the surrounding rings in Au₂₂(SAdm)₁₆ over that in Au₂₁(SAdm)₁₅. Furthermore, with the Ring Model and the grand unified model, two new Au₂₂(SCH₃)₁₆ isomers with evident lower energies, higher HOMO-LUMO gaps as well as distinct optical properties over the available crystallized isomer were obtained. This study deepens the current knowledge on the structure of the Au₂₂(SR)₁₆ cluster from a new structural point of view and also confirms the validity as well as practicability of the Ring Model in understanding and predicting the stable structures of thiolate-protected gold nanoclusters.

Organic Photovoltaic Efficiency Predictor: Data-Driven Models for Non-Fullerene Acceptor Organic Solar Cells

In the design of organic solar cells, there has been a need for materials with high power conversion efficiencies. Scharber's model is commonly used to predict efficiency; however, it exhibits poor performance with new non-fullerene acceptor (NFA) devices, since it was designed for fullerene-based devices. In this work, an empirical model is proposed that can be a more accurate alternative for NFA organic solar cells. Additionally, many screening studies use computationally expensive methods. A model based on using semiempirical simplified time-dependent density functional theory (sTD-DFT) as an alternative method can accelerate the calculations and yield a similar accuracy. The models presented in this paper, termed organic photovoltaic efficiency predictor (OPEP) models, have shown significantly lower errors than previous models, with OPEP/B3LYP yielding errors of 1.53% and OPEP/sTD-DFT of 1.55%. The proposed computational models can be used for the fast and accurate screening of new high-efficiency NFAs/donor pairs.

Computational Evolution of High-Performing Unfused Non-Fullerene Acceptors for Organic Solar Cells

Materials optimization for organic solar cells (OSCs) is a highly active field, with many approaches using empirical experimental synthesis, computational brute-force approaches to screen candidates in a given subset of chemical space, or generative machine learning methods which often require significant training sets. While these methods may find high-performing materials, they can be inefficient and time-consuming. Genetic algorithms (GAs) are an alternative approach, allowing for the "virtual synthesis" of molecules and a prediction of their ``fitness' for some property, with new candidates suggested based on good characteristics of previously generated molecules. In this work, a GA is used to discover high-performing unfused non-fullerene acceptors (NFAs) based on an empirical prediction of power conversion efficiency (PCE) and provides design rules for future work. The electron withdrawing/donating strength, as well as the sequence and symmetry of those units are examined. The utilization of a GA over a brute force approach resulted in speedups up to $1.8 \times 10^{12}$. New types of units not frequently seen in OSCs are suggested, and in total 5,426 NFAs are discovered with the GA. Of these, 1,087 NFAs are predicted to have a PCE greater than 18\%, which is roughly the current record efficiency. While the symmetry of the sequence showed no correlation with PCE, analysis of the sequence arrangement revealed that higher performance can be achieved with a donor core and acceptor end groups. Future NFA designs should consider this strategy as an alternative to the current A-D-A$'$-D-A architecture.

CalcUS: An Open-Source Quantum Chemistry Web Platform

Computational chemistry is an increasingly active field due to the improvement of computing resources and theoretical tools. However, its use remains usually limited to technically inclined users due to the technical challenges of preparing, launching, and analyzing calculations. In this context, we have developed CalcUS, an open-source platform to streamline quantum chemistry studies. Its objective is to democratize access to computational chemistry by providing a user-friendly web interface to simplify running and analyzing quantum mechanical calculations. It is freely available, expandable, and customizable. It promotes connectivity to multiple software packages and algorithms, thus providing state-of-the-art techniques to all practitioners. We propose CalcUS as a standalone tool and infrastructure to support other open-source packages.

Accelerating molecular property calculations with semiempirical preconditioning

Computing ab initio molecular linear response properties, e.g., electronic excitation energies and transition dipole moments, requires the solution of large eigenvalue problems or large systems of equations. These large eigenvalue problems or large systems of equations are commonly solved iteratively using Krylov space algorithms, such as the Davidson algorithm for eigenvalue problems. A critical ingredient in Krylov space algorithms is the preconditioner, which is used to generate optimal update vectors in each iteration. We propose to use semiempirical approximations as preconditioners to accelerate the calculation of ab initio properties. The crucial advantage to improving the preconditioner is that the converged result is unchanged, so there is no trade-off between accuracy and speedup. We demonstrate our approach by accelerating the calculation of electronic excitation energies and electric polarizabilities from linear response time-dependent density functional theory using the simplified time-dependent density functional theory semiempirical model. For excitation energies, the semiempirical preconditioner reduces the number of iterations on average by 37% and up to 70%. The semiempirical preconditioner reduces the number of iterations for computing the polarizability by 15% on average and up to 33%. Moreover, we show that the preconditioner can be further improved by tuning the empirical parameters that define the semiempirical model, leading to an additional reduction in the number of iterations by about 20%. Our approach bridges the gap between semiempirical models and ab initio methods and charts a path toward combining the speed of semiempirical models with the accuracy of ab initio methods.

Self-assembling, structure and nonlinear optical properties of fluorescent organic nanoparticles in water

Owing to their intense emission, low toxicity and solubility in aqueous medium, fluorescent organic nanoparticles (FONs) have emerged as promising alternatives to inorganic ones for the realization of exogenous probes for bioimaging applications. However, the intimate structure of FONs in solution, as well as the role played by intermolecular interactions on their optical properties, remains challenging to study. Following a recent Second-Harmonic Scattering (SHS) investigation led by two of us [Daniel et al., ACS Photonics, 2015, 2, 1209], we report herein a computational study of the structural organization and second-order nonlinear optical (NLO) properties of FONs based on dipolar chromophores incorporating a hydrophobic triphenylamine electron-donating unit and a slightly hydrophilic aldehyde electron-withdrawing unit at their extremities. Molecular dynamics simulations of the FON formation in water are associated with quantum chemical calculations, to provide insight into the molecular aggregation process, the molecular orientation of the dipolar dyes within the nanoparticles, and the dynamical behavior of their NLO properties. Moreover, the impact of intermolecular interactions on the NLO responses of the FONs is investigated by employing the tight-binding version of the recently developed simplified time-dependent density functional theory (sTD-DFT) approach, allowing the all-atom quantum mechanics treatment of nanoparticles.

Closer Look at Inverse Electron Demand Diels–Alder and Nucleophilic Addition Reactions on s-Tetrazines Using Enhanced Sampling Methods

Inverse electron demand [4+2] Diels–Alder (iEDDA) reactions as well as unprecedented nucleophilic (azaphilic) additions of R-substituted silyl-enol ethers (where R is Phenyl, Methyl, and Hydrogen) to 1,2,4,5-tetrazine (s-tetrazine) catalyzed by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3 have recently been discovered (Simon et al. in Org Lett 23(7):2426–2430, 2021), where static calculations were employed for calculation of activation energies. In order to have a more realistic dynamic description of these reactions in explicit solution at ambient conditions, in this work we use a semiempirical tight-binding method combined with enhanced sampling techniques to calculate free energy surfaces (FESs) of the iEDDA and azaphilic addition reactions. Relevant products of not only s-tetrazine but also its derivatives such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3-mediated s-tetrazine adducts are investigated. We reconstruct the FESs of the iEDDA and azaphilic addition reactions using metadynamics and blue moon ensemble, and compare the ability of different collective variables (CVs) including bond distances, Social PeRmutation INvarianT (SPRINT) coordinates, and path-CV to describe the reaction pathway. We find that when a bulky Phenyl is used as a substituent at the dienophile the azaphilic addition is preferred over the iEDDA reaction. In addition, we also investigate the effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3 in the diene and steric hindrance in the dienophile on the competition between the iEDDA and azaphilic addition reactions, providing chemical insight for reaction design.

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.

Perspective on Simplified Quantum Chemistry Methods for Excited States and Response Properties

We review recent developments in the framework of simplified quantum chemistry for excited state and optical response properties (sTD-DFT) and present future challenges for new method developments to improve accuracy and extend the range of application. In recent years, the scope of sTD-DFT was extended to molecular response calculations of the polarizability, optical rotation, first hyperpolarizability, two-photon absorption (2PA), and excited-state absorption for large systems with hundreds to thousands of atoms. The recently introduced spin-flip simplified time-dependent density functional theory (SF-sTD-DFT) variant enables an ultrafast treatment for diradicals and related strongly correlated systems. A few drawbacks were also identified, specifically for the computation of 2PA cross sections. We propose solutions to this problem and how to generally improve the accuracy of simplified schemes. New possible simplified schemes are also introduced for strongly correlated systems, e.g., with a second-order perturbative correlation correction. Interpretation tools that can extract chemical structure-property relationships from excited state or response calculations are also discussed. In particular, the recently introduced method-agnostic RespA approach based on natural response orbitals (NROs) as the key concept is employed.

Nonlinear light absorption in many-electron systems excited by an instantaneous electric field: a non-perturbative approach

Applications of low-cost non-perturbative approaches in real time, such as time-dependent density functional theory, for the study of nonlinear optical properties of large and complex systems are gaining increasing popularity. However, their assessment still requires the analysis and understanding of elementary dynamical processes in simple model systems. Motivated by the aim of simulating optical nonlinearities in molecules, here exemplified by the case of the quaterthiophene oligomer, we investigate light absorption in many-electron interacting systems beyond the linear regime by using a single broadband impulse of an electric field; i.e. an electrical impulse in the instantaneous limit. We determine non-pertubatively the absorption cross section from the Fourier transform of the time-dependent induced dipole moment, which can be obtained from the time evolution of the wavefunction. We discuss the dependence of the resulting cross section on the magnitude of the impulse and we highlight the advantages of this method in comparison with perturbation theory by working on a one-dimensional model system for which numerically exact solutions are accessible. Thus, we demonstrate that the considered non-pertubative approach provides us with an effective tool for investigating fluence-dependent nonlinear optical excitations.

Combining Graphics Processing Units, Simplified Time-Dependent Density Functional Theory, and Finite-Difference Couplings to Accelerate Nonadiabatic Molecular Dynamics

Starting from our recently published implementation of nonadiabatic molecular dynamics (NAMD) on graphics processing units (GPUs), we explore further approaches to accelerate ab initio NAMD calculations at the time-dependent density functional theory (TDDFT) level of theory. We employ (1) the simplified TDDFT schemes of Grimme et al. and (2) the Hammes-Schiffer-Tully approach to obtain nonadiabatic couplings from finite-difference calculations. The resulting scheme delivers an accurate physical picture while virtually eliminating the two computationally most demanding steps of the algorithm. Combined with our GPU-based integral routines for SCF, TDDFT, and TDDFT derivative calculations, NAMD simulations of systems of a few hundreds of atoms at a reasonable time scale become accessible on a single compute node. To demonstrate this and to present a first, illustrative example, we perform TDDFT/MM-NAMD simulations of the rhodopsin protein.

Optical limiting properties, structure and simplified TD-DFT calculations of scandium tetra-15-crown-5 phthalocyaninates

The optical limiting properties of crown-ether-substituted scandium(III) phthalocyaninate complexes, bis-tetra-15-crown-5-phthalocyaninates Sc[(15C5)4Pc][Formula: see text] (I) and Sc[(15C5)4Pc][Formula: see text] (Ia), together with monophthalocyaninate [(15C5)4Pc]Sc(OAc) (II) were measured by using the Z-scan technique (532 nm laser and pulse rate of 10 ns). It was revealed that expansion of the [Formula: see text]-system on moving from the monomeric Sc complex II to sandwich compound I and changing the electronic state of the sandwich compound from the anionic Ia species to the neutral radical I improves the optical limiting properties. The Im[[Formula: see text]] values obtained lie in the 10[Formula: see text]–10[Formula: see text] esu range that is consistent with those reported previously for other organic chromophores. The crystal structure of sandwich Sc(III) complex I was elucidated by means of single-crystal X-ray diffraction analysis and was used to guide a series of theoretical calculations. It was demonstrated that the application of simplified time-dependent density functional theory (sTD-DFT) calculations can provide reasonably accurate predictions for compounds of this type when the geometries of the complexes are clearly defined.

Synergistic Approach of Ultrafast Spectroscopy and Molecular Simulations in the Characterization of Intramolecular Charge Transfer in Push-Pull Molecules

The comprehensive characterization of Intramolecular Charge Transfer (ICT) stemming in push-pull molecules with a delocalized π-system of electrons is noteworthy for a bespoke design of organic materials, spanning widespread applications from photovoltaics to nanomedicine imaging devices. Photo-induced ICT is characterized by structural reorganizations, which allows the molecule to adapt to the new electronic density distribution. Herein, we discuss recent photophysical advances combined with recent progresses in the computational chemistry of photoactive molecular ensembles. We focus the discussion on femtosecond Transient Absorption Spectroscopy (TAS) enabling us to follow the transition from a Locally Excited (LE) state to the ICT and to understand how the environment polarity influences radiative and non-radiative decay mechanisms. In many cases, the charge transfer transition is accompanied by structural rearrangements, such as the twisting or molecule planarization. The possibility of an accurate prediction of the charge-transfer occurring in complex molecules and molecular materials represents an enormous advantage in guiding new molecular and materials design. We briefly report on recent advances in ultrafast multidimensional spectroscopy, in particular, Two-Dimensional Electronic Spectroscopy (2DES), in unraveling the ICT nature of push-pull molecular systems. A theoretical description at the atomistic level of photo-induced molecular transitions can predict with reasonable accuracy the properties of photoactive molecules. In this framework, the review includes a discussion on the advances from simulation and modeling, which have provided, over the years, significant information on photoexcitation, emission, charge-transport, and decay pathways. Density Functional Theory (DFT) coupled with the Time-Dependent (TD) framework can describe electronic properties and dynamics for a limited system size. More recently, Machine Learning (ML) or deep learning approaches, as well as free-energy simulations containing excited state potentials, can speed up the calculations with transferable accuracy to more complex molecules with extended system size. A perspective on combining ultrafast spectroscopy with molecular simulations is foreseen for optimizing the design of photoactive compounds with tunable properties.

Insights into the halochromism of a bithiophene π* probe

The positive halochromism of the solvatochromic 4-nitro-4'-(N,N-dimethylamino)-2,2'-bithiophene in acetone and 1-butanol was investigated by molecular dynamics simulations and quantum mechanics calculations. Interactions of the dye with the solvated sodium cation were found to have only a minor effect on the observed halochromism, which was ultimately ascribed to a predominant interaction between iodide anions and the N,N-dimethylamino group of the dye.

Methodological Survey of Simplified TD-DFT Methods for Fast and Accurate Interpretation of UV-Vis-NIR Spectra of Phthalocyanines

A methodological survey of density functional theory (DFT) methods for the prediction of UV-visible (vis)-near-infrared (NIR) spectra of phthalocyanines is reported. Four methods, namely, full time-dependent (TD)-DFT and its Tamm-Dancoff approximation (TDA), together with their simplified modifications (sTD-DFT and sTDA, respectively), were tested by using the examples of unsubstituted and alkoxy-substituted metal-free ligands and zinc complexes. The theoretical results were compared with experimental data derived from UV-visible absorption and magnetic circular dichroism spectroscopy. Seven popular exchange-correlation functionals (BP86, B3LYP, TPSSh, M06, CAM-B3LYP, LC-BLYP, and ωB97X) were tested within these four approaches starting at a relatively modest level using 6-31G(d) basis sets and gas-phase BP86/def2-SVP optimized geometries. A gradual augmentation of the computational levels was used to identify the influence of starting geometry, solvation effects, and basis sets on the results of TD-DFT and sTD-DFT calculations. It was found that although these factors do influence the predicted energies of the vertical excitations, they do not affect the trends predicted in the spectral properties across series of structurally related substituted free bases and metallophthalocyanines. The best accuracy for the gas-phase vertical excitations was observed in the lower-energy Q-band region for calculations that made use of range-separated hybrids for both full and simplified TD-DFT approaches. The CAM-B3LYP functional provided particularly accurate results in the context of the sTD-DFT approach. The description of the higher-energy B-band region is considerably less accurate, and this demonstrates the need for further advances in the accuracy of theoretical calculations. Together with a general increase in accuracy, the application of simplified TD-DFT methods affords a 2-3 orders of magnitude speedup of the calculations in comparison to the full TD-DFT approach. It is anticipated that this approach will be widely used on desktop computers during the interpretation of UV-vis-NIR spectra of phthalocyanines and related macrocycles in the years ahead.

First molecular electronic hyperpolarizability of series of π-conjugated oxazole dyes in solution: an experimental and theoretical study

In this work, we report for the first time, the experimental and theoretical first molecular electronic hyperpolarizability of eleven π-conjugated oxazoles compounds in toluene medium, by using the hyper-Rayleigh scattering (HRS) technique.

Use of Density Functional Based Tight Binding Methods in Vibrational Circular Dichroism

Vibrational circular dichroism (VCD) is a spectroscopic technique used to resolve the absolute configuration of chiral systems. Obtaining a theoretical VCD spectrum requires computing atomic polar and axial tensors on top of the computationally demanding construction of the force constant matrix. In this study we evaluated a VCD model in which all necessary quantities are obtained with density functional based tight binding (DFTB) theory. The analyzed DFTB parametrizations fail at providing accurate vibrational frequencies and electric dipole gradients but yield reasonable normal modes at a fraction of the computational cost of density functional theory (DFT). Thus, by applying DFTB in composite methods along with DFT, we show that it is possible to obtain accurate VCD spectra at a much lower computational demand.