Computing Excited States of Very Large Systems with Range-Separated Hybrid Functionals and the Exact Integral Simplified Time-Dependent Density Functional Theory (XsTD-DFT).

Simplified quantum chemistry (sQC) methods can routinely compute excited states for very large systems in an "all-atom" fashion. They are viable alternatives to regular multiscale schemes. sQC methods have the advantage of accounting explicitly for all of the environment at a quantum mechanical (QM) level.

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).

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 -stilbene and typical fluorescent protein chromophores.

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 , , 2015, , 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.

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.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods.

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 Unified Strategy for the Chemically Intuitive Interpretation of Molecular Optical Response Properties.

Interpreting response properties such as the polarizability, optical rotation (OR), or hyperpolarizabilities is a complex task for which a uniform strategy would be desirable. We propose a response analysis procedure called the RespA approach with two interrelated schemes to describe molecular optical response properties in terms of natural response orbitals (NROs) and chemical fragment response for convenient elucidation of structure-(optical)property relationships. These quantities can be easily extracted from the frequency-dependent perturbed one-electron transition/current density matrix obtained from any quantum mechanical response function calculation.

Simplified time-dependent density functional theory (sTD-DFT) for molecular optical rotation.

Theoretical methods able to screen large sets (e.g., conformers) of possibly large compounds are needed in many typical quantum chemistry applications.

Dynamic Structural Effects on the Second-Harmonic Generation of Tryptophane-Rich Peptides and Gramicidin A.

Peptide chains can model endogenous biotags for applications in second-harmonic imaging microscopy. Such structures are flexible which may strongly affect their structure-property relationship. Here, we explore quantum-mechanically the conformational space of a set of tryptophan-rich model peptides.

Are Fully Conjugated Expanded Indenofluorenes Analogues and Diindeno[]thiophene Derivatives Diradicals? A Simplified (Spin-Flip) Time-Dependent Density Functional Theory [(SF-)sTD-DFT] Study.

Polycyclic hydrocarbons are often used to understand the electronic structure of nanographene systems. Among them, indeno[1,2]fluorene and indeno[1,2]fluorene isomers present a central -quinodimethane unit leading to unique optical properties. In this work, we characterized the absorption spectra of indeno[1,2]fluorene and [2,1-]diindeno[]thiophene derivatives with (spin-flip) simplified time-dependent density functional theory [(SF-)sTD-DFT] methods.

A Simplified Spin-Flip Time-Dependent Density Functional Theory Approach for the Electronic Excitation Spectra of Very Large Diradicals.

Experimentalists working with diradicals are often facing the question of what kind of species among singlet or triplet diradicals or closed-shell molecules are observed. To treat large diradicals with a high density of electronic states, we propose a simplified version of the spin-flip time-dependent density functional theory (SF-TD-DFT) method for a fast computation of their state energies and absorption spectra with an accuracy similar to the nonsimplified scheme. An ultrafast tight-binding variant called SF-sTD-DFT-xTB is also developed to treat even larger systems.

Nonlinear-response properties in a simplified time-dependent density functional theory (sTD-DFT) framework: Evaluation of excited-state absorption spectra.

The energy conversion efficiency of organic solar cells seems crucial for a clean future. The design of new light-harvesting devices needs an in-depth understanding of their optical properties, including the excited-state absorption (ESA). In biology, the optical characterization of photochemical/physical processes happening in photosynthetic pigments and proteins can be difficult to interpret due to their structural complexities.

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.

ONIOM Investigation of the Second-Order Nonlinear Optical Responses of Fluorescent Proteins.

The first hyperpolarizability (β) of six fluorescent proteins (FPs), namely, enhanced green fluorescent protein, enhanced yellow fluorescent protein, SHardonnay, ZsYellow, DsRed, and mCherry, has been calculated to unravel the structure-property relationships on their second-order nonlinear optical properties, owing to their potential for multidimensional biomedical imaging. The ONIOM scheme has been employed and several of its refinements have been addressed to incorporate efficiently the effects of the microenvironment on the nonlinear optical responses of the FP chromophore that is embedded in a protective β-barrel protein cage. In the ONIOM scheme, the system is decomposed into several layers (here two) treated at different levels of approximation (method1/method2), from the most elaborated method (method1) for its core (called the high layer) to the most approximate one (method2) for the outer surrounding (called the low layer).

Two-photon absorption spectroscopy of stilbene and phenanthrene: Excited-state analysis and comparison with ethylene and toluene.

Two-photon absorption (2PA) spectra of several prototypical molecules (ethylene, toluene, trans- and cis-stilbene, and phenanthrene) are computed using the equation-of-motion coupled-cluster method with single and double substitutions. The states giving rise to the largest 2PA cross sections are analyzed in terms of their orbital character and symmetry-based selection rules. The brightest 2PA transitions correspond to Rydberg-like states from fully symmetric irreducible representations.

Two-photon absorption spectroscopy of trans-stilbene, cis-stilbene, and phenanthrene: Theory and experiment.

Two-photon absorption (2PA) spectroscopy provides complementary, and sometimes more detailed, information about the electronic structure of a molecule relative to one-photon absorption (1PA) spectroscopy. However, our understanding of the 2PA processes is rather limited due to technical difficulties in measuring experimental 2PA spectra and theoretical challenges in computing higher-order molecular properties. This paper examines the 2PA spectroscopy of trans-stilbene, cis-stilbene, and phenanthrene by a combined experimental and theoretical approach.

Approximate Spin-Projected Density-Based Romberg Differentiation Procedure to Evaluate the Second-Hyperpolarizability of p-Quinodimethane and Twisted Ethylene and Their Diradical Character Dependence.

The evaluation of the static second hyperpolarizability (γ) of diradical species is a challenging task due to the use of spin-unrestricted methods, which may suffer from spin contamination. Here, we present the methodological aspect of a density-based differentiation procedure to evaluate static polarizability and hyperpolarizabilities. The finite-field calculations are done on the spin-projected electron density to remove the spin contamination, and the automatized Romberg's differentiation procedure is used to improve the numerical accuracy in the finite-field method.

Challenging compounds for calculating molecular second hyperpolarizabilities: the triplet state of the trimethylenemethane diradical and two derivatives.

The second hyperpolarizability γ of trimethylenemethane (TMM) and two 1,3-dipole derivatives (NXA and OXA) in their triplet ground state has been evaluated at the UCCSD(T) level with the d-aug-cc-pVDZ extended basis set, highlighting that γ decreases from TMM to NXA and OXA, following the opposite order of their permanent dipole moments. These results are then used to benchmark a broad range of levels of approximation. So, the UMP2, UMP4, and UCCSD methods can be used to characterize γ of TMM and NXA but not of OXA.

Frequency dispersion of the first hyperpolarizabilities of reference molecules for nonlinear optics.

The frequency dispersion of the hyper-Rayleigh scattering first hyperpolarizabilities (βHRS) of five reference molecules for nonlinear optics, namely, carbon tetrachloride, chloroform, dichloromethane, acetonitrile, and trichloroacetonitrile, is described using the coupled-cluster singles and doubles quadratic response function (CCSD-QRF) as well as approximate schemes. Comparisons to approximate schemes in which the frequency dispersion is evaluated as either a multiplicative or an additive correction to the static hyperpolarizability yield the following observations: (i) errors of the order of 10% or less are usually encountered when using the multiplicative scheme for photon energies far from the lowest dipole-allowed excitation energies, (ii) spurious cases cannot be excluded as evidenced by carbon tetrachloride where the multiplicative scheme predicts a decrease of βHRS in contradiction to the increase obtained using the CCSD-QRF method, and (iii) the additive scheme is at best as reliable as the multiplicative approximation. The two-state approximation presents the advantage of correcting the wrong behavior of the additive and multiplicative schemes for carbon tetrachloride, but it is not an improved solution for the other compounds, while the question of selecting the appropriate dominant excited state remains unanswered.

Challenging compounds for calculating hyperpolarizabilities: p-quinodimethane derivatives.

The hyperpolarizabilities of three p-quinodimethane derivatives with low diradical character have been evaluated. As electron correlation effects rule the electric field response properties, wave function and density functional theory-based methods have been compared to benchmark values calculated with the coupled cluster method including single and double excitations as well as perturbative estimate of the triples [CCSD(T)]. The basis set effects have been further assessed.

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.

Electron correlation effects on the first hyperpolarizability of push-pull π-conjugated systems.

The first hyperpolarizability (β) of representative push-pull π-conjugated compounds has been calculated at several levels of approximation to assess the effects of electron correlation. First, the 6-31+G(d) basis set has been shown to give the best balance between accuracy and computational resources for a polyene linker whereas for polyyne linker, the 6-31G(d) basis set is already an optimal choice. As a result of cancellations between higher order contributions, the MP2 method turns out to be the method of choice to predict β of push-pull π-conjugated systems since it closely reproduces the values obtained with the reference CCSD(T) scheme.