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-<i>aug</i>-cc-pVQZ and <i>aug</i>-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 <i>ab initio</i> post-Hartree–Fock quantum-chemistry approaches (including the coupled cluster method) to calculate electronic and nuclear relaxation (hyper)­polarizabilities of carbon dioxide, formaldehyde, <i>cis</i>-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 <i>aug</i>-cc-pVDZ basis set (5.3%), although for more accurate calculations of vibrational contributions, i.e., average absolute errors less than 1%, the <i>aug</i>-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 <i>aug</i>-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 <i>aug</i>-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

Chelation-Induced Quenching of Two-Photon Absorption of Azacrown Ether Substituted Distyryl Benzene for Metal Ion Sensing

Imaging of metal ion concentration, distribution, and dynamics can pave the way to diagnose a number of diseases and to identify the normal functioning of the human body. Recently, two-photon microscopy-based imaging of metal ions has become popular due to several favorable factors as compared to fluorescence-based imaging. However, much has to be investigated in order to design probes with large two-photon absorption cross sections and yet with selective binding affinity toward metal ions. In particular, it is crucial to recognize the mechanisms of metal ion-induced changes of the two-photon absorption intensity. The present paper contributes to this effort and reports on the results of extensive studies carried out to define a reliable computational protocol that can account for sampling, solvent, and finite temperature effects for one- and two-photon properties of metal probes, using azacrown ether substituted distyrylbenzene embedded in solvents as a testbed. We employ a selection of theoretical approaches to model the structure of the probe alone and in the presence of Mg²⁺ ion in acetonitrile solvent, including static quantum-chemical calculations, rigid- and flexible-body molecular dynamics, and hybrid QM/MM molecular dynamics. For a set of solute–solvent configurations, the one- and the two-photon properties are computed using the recently developed polarizable embedding response approach. It is found that the hybrid QM/MM molecular dynamics based approach is the most successful one among other employed computational strategies, viz. reproduction of the metal ion-induced blue shift in the absorption wavelength and decrease in the two-photon absorption cross section, which actually is in excellent agreement with experimental data. The mechanism for such metal ion-induced changes in the optical properties is put forward using a few-state model. Possible design principles to tune the two-photon absorption properties of probes are also discussed

Quantifying the Performances of DFT for Predicting Vibrationally Resolved Optical Spectra: Asymmetric Fluoroborate Dyes as Working Examples

This article aims at a quantitative assessment of the performances of a panel of exchange-correlation functionals, including semilocal (BLYP and PBE), global hybrids (B3LYP, PBE0, M06, BHandHLYP, M06-2X, and M06-HF), and range-separated hybrids (CAM-B3LYP, LC-ωPBE, LC-BLYP, ωB97X, and ωB97X-D), in predicting the vibrationally resolved absorption spectra of BF₂-carrying compounds. To this end, for 19 difluoroborates as examples, we use, as a metric, the vibrational reorganization energy (λ_vib) that can be determined based on the computationally efficient linear coupling model (a.k.a. vertical gradient method). The reference values of λ_vib were determined by employing the CC2 method combined with the cc-pVTZ basis set for a representative subset of molecules. To validate the performances of CC2, comparisons with experimental data have been carried out as well. This study shows that the vibrational reorganization energy, involving Huang–Rhys factors and normal-mode frequencies, can indeed be used to quantify the reliability of functionals in the calculations of the vibrational fine structure of absorption bands, i.e., an accurate prediction of the vibrational reorganization energy leads to absorption band shapes better fitting the selected reference. The CAM-B3LYP, M06-2X, ωB97X-D, ωB97X, and BHandHLYP functionals all deliver vibrational reorganization energies with absolute relative errors smaller than 20% compared to CC2, whereas 10% accuracy can be achieved with the first three functionals. Indeed, the set of examined exchange-correlation functionals can be divided into three groups: (i) BLYP, B3LYP, PBE, PBE0, and M06 yield inaccurate band shapes (λ_vib,TDDFT < λ_vib,CC2), (ii) BHandHLYP, CAM-B3LYP, M06-2X, ωB97X, and ωB97X-D provide accurate band shapes (λ_vib,TDDFT ≈ λ_vib,CC2), and (iii) LC-ωPBE, LC-BLYP, and M06-HF deliver rather poor band topologies (λ_vib,TDDFT > λ_vib,CC2). This study also demonstrates that λ_vib can be reliably estimated using the CC2 model and the relatively small cc-pVDZ basis set. Therefore, the linear coupling model combined with the CC2/cc-pVDZ level of theory can be used as a very efficient approach to determine λ_vib values that can be used to select the most adequate functional for more accurate vibronic calculations, e.g., including more refined models and environmental effects

Resonant and Nonresonant Hyperpolarizabilities of Spatially Confined Molecules: A Case Study of Cyanoacetylene

In this theoretical study we report on resonant and nonresonant electric-dipole (hyper)­polarizabilities of cyanoacetylene molecule confined by repulsive potentials of cylindrical symmetry mimicking a topology of nanotubelike carbon cages. The set of investigated electronic properties encompasses dipole moment, polarizability, first and second hyperpolarizability as well as the two-photon transition matrix elements. The effect of external potential on vibrational contributions to electric-dipole properties is also included in our treatment. The computations are performed at several levels of theoretical approximation including state-of-the-art coupled-cluster (CCSD­(T)) and multireference configuration interaction methods (MRCISD­(Q)). The results of calculations presented herein indicate that the decrease in dipole moment observed experimentally for the HCCCN molecule solvated in helium nanodroplets may be partially attributed to the confinement effects. The external confining potential causes a substantial drop of the isotropic average electronic polarizability and second hyperpolarizability. In contrast, the vector component of the electronic first hyperpolarizability substantially increases. Nuclear relaxation contributions to all studied electric-dipole properties are found to diminish upon confinement. Our calculations also indicate that the most intense ¹Σ⁺ ← <i>X̃</i> one-photon transition is slightly blue-shifted whereas the corresponding oscillator strength is virtually unaffected upon confinement. Interestingly, the absolute magnitude of the diagonal component of the second-order transition moment for the bright state (<i>S</i>_<i>zz</i>^0→¹∑⁺) increases with the strength of external potential. The effect of structural relaxation on the electric-dipole properties, arising from the presence of the external potential, is also investigated in the present work

Toward Fully Nonempirical Simulations of Optical Band Shapes of Molecules in Solution: A Case Study of Heterocyclic Ketoimine Difluoroborates

This study demonstrates that a hybrid density functional theory/molecular mechanics approach can be successfully combined with time-dependent wavepacket approach to predict the shape of optical bands for molecules in solutions, including vibrational fine structure. A key step in this treatment is the estimation of the inhomogeneous broadening based on the hybrid approach, where the polarization between solute and atomically decomposed solvent is taken into account in a self-consistent manner. The potential of this approach is shown by predicting optical absorption bands for three heterocyclic ketoimine difluoroborates in solution

Revealing the Electronic and Molecular Structure of Randomly Oriented Molecules by Polarized Two-Photon Spectroscopy

In this Letter, we explored the use of polarized two-photon absorption (2PA) spectroscopy, which brings additional information when compared to methods that do not use polarization control, to investigate the electronic and molecular structure of two chromophores (<b>FD43</b> and <b>FD48</b>) based on phenylacetylene moieties. The results were analyzed using quantum chemical calculations of the two-photon transition strengths for circularly and linearly polarized light, provided by the response function formalism. On the basis of these data, it was possible to distinguish and identify the excited electronic states responsible for the lowest-energy 2PA-allowed band in both chromophores. By modeling the 2PA circular–linear dichroism, within the sum-over-essential states approach, we obtained the relative orientation between the dipole moments that are associated with the molecular structure of the chromophores in solution. This result allowed to correlate the V-shape structure of the <b>FD48</b> chromophore and the quantum-interference-modulated 2PA strength

Experimental and Theoretical Study on the One- and Two-Photon Absorption Properties of Novel Organic Molecules Based on Phenylacetylene and Azoaromatic Moieties

This Article reports a combined experimental and theoretical analysis on the one and two-photon absorption properties of a novel class of organic molecules with a π-conjugated backbone based on phenylacetylene (<b>JCM874</b>, <b>FD43</b>, and <b>FD48</b>) and azoaromatic (<b>YB3p25</b>) moieties. Linear optical properties show that the phenylacetylene-based compounds exhibit strong molar absorptivity in the UV and high fluorescence quantum yield with lifetimes of approximately 2.0 ns, while the azoaromatic-compound has a strong absorption in the visible region with very low fluorescence quantum yield. The two-photon absorption was investigated employing nonlinear optical techniques and quantum chemical calculations based on the response functions formalism within the density functional theory framework. The experimental data revealed well-defined 2PA spectra with reasonable cross-section values in the visible and IR. Along the nonlinear spectra we observed two 2PA allowed bands, as well as the resonance enhancement effect due to the presence of one intermediate one-photon allowed state. Quantum chemical calculations revealed that the 2PA allowed bands correspond to transitions to states that are also one-photon allowed, indicating the relaxation of the electric-dipole selection rules. Moreover, using the theoretical results, we were able to interpret the experimental trends of the 2PA spectra. Finally, using a few-energy-level diagram, within the sum-over-essential states approach, we observed strong qualitative and quantitative correlation between experimental and theoretical results