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. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design.

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. Moreover, the SDQ-MP4 and CCSD approaches provide rarely improved estimates over MP2 while the MP4 method does not represent an improvement over MP4-SDQ or the SCS-MP2 method, over MP2. Among density functional theory exchange-correlation functionals, LC-BLYP is reliable when characterizing the changes of first hyperpolarizability upon enlarging the π-conjugated linker or upon changing the polyyne linker into a polyene segment. Nevertheless, its reliability is very similar to what can be achieved with the Hartree-Fock method and the MP2 scheme is by far more accurate. On the other hand, the BLYP, B3LYP, and BHandHLYP functionals perform quantitatively better in a number of cases but the trends are poorly described. This is also the case of the B2-PLYP and mPW2-PLYP functionals, which are often the most accurate, though they underestimate the increase of β when going from polyyne to polyene linkers and overestimate the enhancement of β with chain length.

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

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

By considering two prototypical π‐conjugated compounds, several technical aspects associated with the evaluation of the first hyperpolarizabilities have been addressed in this article, that is, (i) the automatization of the Romberg's scheme to improve the numerical accuracy in the finite field method, (ii) the evaluation of the frequency dispersion at correlated levels using approximate schemes, and (iii) the deviations from Kleinman's symmetry conditions. It results from this study that accurate numerical derivatives can be obtained by resorting to the Romberg's method and by analyzing the Romberg's table in terms of two quantities, the field error and the iteration error. Indeed, the resulting first hyperpolarizability values are in close agreement with those obtained using an analytical differentiation procedure. The reliability of the multiplicative and additive approximate schemes to describe the frequency dispersion at correlated levels from using HF (Hartree‐Fock) frequency dispersion has been confirmed to be limited to large wavelengths or far‐from‐resonance wavelength regions. Kleinman's symmetry conditions have been assessed, showing that for off‐diagonal components of these two π‐conjugated compounds, the deviations could be substantial. Nevertheless, good accuracy can be achieved for experimentally related quantities like βHRS because the diagonal tensor components are dominant. © 2014 Wiley Periodicals, Inc.