Assessment of DFT Exchange–Correlation Functionals for Evaluating the Multipolar Contributions to the Quadratic Nonlinear Optical Responses of Small Reference Molecules

Disentangling the molecular polarizability and first hyperpolarizability of methanol-air interfaces

Liquid-air interfaces have extensive implications in different areas of interest because the dynamical processes at the interface can be different from those in bulk. Thus, its characterization, understanding, and control may be pivotal in advancing discoveries. However, characterizing the interface requires special and selective tools to avoid signals from the bulk region. This surface specificity and versatility is achieved by using the second harmonic generation (SHG) responses. This study adopts multiscale simulation methods to evaluate the surface SHG responses of methanol-air interfaces with submonolayer resolution tackled by sequentially using classical molecular dynamics simulations under different temperatures and then employing quantum chemistry methods to compute the molecular first hyperpolarizabilities (β). This approach ensures the configurational diversity required to evaluate the average β values. The main achievements are (i) a quasi-absence of surface sensitivity of the mean polarizability 〈α〉 with values about 2% larger than those obtained in bulk, (ii) conversely, smooth variations on the polarizability anisotropy Δα are observed up to the fourth molecular layer at around 20 Å from the interface, and (iii) narrow interfacial effects on the SHG responses, β(-2ω;ω,ω), which are limited to the first molecular layer (∼3.0 Å) and characterized by a high contrast in the βZZZ(-2ω;ω,ω) tensor component between the first and the subsequent layers. Similar trends are obtained at different temperatures or when increasing the number of methanol molecules treated at the quantum chemistry level, indicating the robustness of the approach for describing the dipolar molecular responses of air-liquid interfaces.

Frequency-dependent nonlinear optical response and refractive index investigation of lactone-derived thermochromic compounds

Nonlinear optical (NLO) switchable materials play a crucial role in the fields of electronics and optoelectronics. The selection of an appropriate switching approach is vital in designing such materials to enhance their NLO response. Among various approaches, thermos-switching materials have shown a 4-fold increase in NLO response compared to other photo-switching materials. In this study, we computationally investigated the geometric, electronic, and nonlinear optical properties of reversible lactone-based thermochromic compounds using the ωB97XD/6-311+G (d,p) level of theory. Molecular orbital studies are employed to analyze the electronic properties of the close and open isomers of these compounds, while time-dependent density functional theory (TD-DFT) analysis is utilized to evaluate their molecular absorption. Our findings reveal that the π-electronic conjugation-induced delocalization significantly influences the ON-OFF switchable nonlinear optical response of the lactone-based thermochromic compounds. Notably, among all compounds, the open isomer of lactone 2 exhibits the highest hyperpolarizability value (6596.69 au). Furthermore, we extended our analysis to investigate the frequency-dependent second and third-order hyperpolarizabilities. The most pronounced frequency-dependent NLO response is observed at 532 nm. Additionally, we calculated the refractive index of these thermochromic compounds to further assess their nonlinear optical response. The open isomer of lactone 1 demonstrates the highest refractive index value (3.99 × 10-14 cm2/W). Overall, our study highlights the excellent potential of reversible thermochromic compounds as NLO molecular thermos-switches for future applications.

First-principles evaluation of the second harmonic generation response of reference organic and inorganic crystals

Using the CRYSTAL17 package at the coupled-perturbed Kohn-Sham (CPKS) level, periodic boundary conditions first-principles calculations are enacted to predict the second harmonic generation second-order nonlinear optical (NLO) susceptibility, χ⁽²⁾, values of six historical NLO crystals. This selection allowed the comparison between state-of-the-art calculations and experiment. Several computational aspects are tackled to define conditions where the results are converged with respect to the range of lattice summations, to the number of k-points in the first Brillouin zone, to the order of the multipole expansions for evaluating the long-range part of the electrostatic interactions, as well as to the atomic basis set size. A valence triple zeta basis set supplemented with polarization functions has been selected. Then, χ⁽²⁾ calculations have been performed using a range of exchange-correlation functionals (XCFs). Results show the large impact of the amount of Hartree-Fock (HF) exchange on the amplitude but also on the sign on the χ⁽²⁾ tensor components. To a given extent, these amplitude effects are consistent with results on molecules, but the sign reversal effects and the non-monotonic behavior of the χ⁽²⁾ tensor components as a function of the amount of HF exchange are scarcely found for molecules. Then, using the recommended range-separated hybrid XCFs, the CPKS scheme leads to good agreement with experimental data for potassium dihydrogenophosphate, urea, and χ_ZXX ⁽²⁾ of LiNbO₃. The agreement is more questionable for χ_ZZZ ⁽²⁾ of LiNbO₃ whereas it remains poor for ammonium dihydrogenophosphate and 2-methyl-4-nitroaniline, with large underestimations by about a factor of 3, opening a path to further fine-tuning of the ranges of inclusion of HF exchange.

Investigation of the Second Harmonic Generation at the Water-Vacuum Interface by Using Multi-Scale Modeling Methods

The Sequential Quantum Mechanics/Molecular Mechanics scheme has been enacted to perform a systematic investigation of the polarizability (α) and first hyperpolarizability (β) responses at the water-vacuum interface. After performing classical molecular dynamics simulations to provide snapshots of the structures, quantum chemistry calculations of the linear and nonlinear optical responses have been performed for clusters of five water molecules at the time-dependent DFT level in combination with different embedding schemes, ranging from point charges to polarizable point charges, with and without local field effects. When going from the bulk to the interface, the main observations of these calculations encompass i) a modest increase of the average polarizability but an increase by about a factor of two of its anisotropy, ii) an increase by about 20 % of the β_HRS response, accompanied by a small increase of its depolarization ratio, and iii) a net increase of the component of the β tensor normal to the interface (β_zzz ) as well as of β_// . Globally, the interfacial effects on β are localized at the first molecular layer while they are observed up to the fourth molecular layer on α.

Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

In the past several decades, density functional theory (DFT) has evolved as a leading player across a dazzling variety of fields, from organic chemistry to condensed matter physics. The simple conceptual framework and computational elegance are the underlying driver for this. This article reviews some of the recent developments that have taken place in our laboratory in the past 5 years. Efforts are made to validate a viable alternative for DFT calculations for small to medium systems through a Cartesian coordinate grid- (CCG-) based pseudopotential Kohn–Sham (KS) DFT framework using LCAO-MO ansatz. In order to legitimize its suitability and efficacy, at first, electric response properties, such as dipole moment (μ), static dipole polarizability (α), and first hyperpolarizability (β), are calculated. Next, we present a purely numerical approach in CCG for proficient computation of exact exchange density contribution in certain types of orbital-dependent density functionals. A Fourier convolution theorem combined with a range-separated Coulomb interaction kernel is invoked. This takes motivation from a semi-numerical algorithm, where the rate-deciding factor is the evaluation of electrostatic potential. Its success further leads to a systematic self-consistent approach from first principles, which is desirable in the development of optimally tuned range-separated hybrid and hyper functionals. Next, we discuss a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, by means of “adiabatic connection theorem” and virial theorem. Optical gaps in organic chromophores, dyes, linear/non-linear PAHs, and charge transfer complexes are faithfully reproduced. In short, CCG-DFT is shown to be a successful route for various practical applications in electronic systems.

First hyperpolarizability of water at the air-vapor interface: a QM/MM study questions standard experimental approximations

Surface Second-Harmonic Generation (S-SHG) experiments provide a unique approach to probe interfaces. One important issue for S-SHG is how to interpret the S-SHG intensities at the molecular level. Established frameworks commonly assume that each molecule emits light according to an average molecular hyperpolarizability tensor β(-2ω,ω,ω). However, for water molecules, this first hyperpolarizability is known to be extremely sensitive to their environment. We have investigated the molecular first hyperpolarizability of water molecules within the liquid-vapor interface, using a quantum description with explicit, inhomogeneous electrostatic embedding. The resulting average molecular first hyperpolarizability tensor depends on the distance relative to the interface, and it practically respects the Kleinman symmetry everywhere in the liquid. Within this numerical approach, based on the dipolar approximation, the water layer contributing to the Surface Second Harmonic Generation (S-SHG) intensity is less than a nanometer. The results reported here question standard interpretations based on a single, averaged hyperpolarizability for all molecules at the interface. Not only the molecular first hyperpolarizability tensor significantly depends on the distance relative to the interface, but it is also correlated to the molecular orientation. Such hyperpolarizability fluctuations may impact the S-SHG intensity emitted by an aqueous interface.

Impact of van der Waals interactions on the structural and nonlinear optical properties of azobenzene switches

The geometrical structures, relative Z-E energies, and second-order nonlinear responses of a collection of azobenzene molecules symmetrically substituted in the meta-position with functional groups of different bulkiness are investigated using various ab initio and density functional approximations. We show that RI-MP2 and RI-CC2 approximations provide very similar geometries and relative energies and evidence that London dispersion interactions existing between bulky meta-substituents stabilize the Z conformer. The ωB97X-D exchange-correlation functional provides an accurate description of these effects and gives a good account of the nonlinear optical response of the molecules. We show that density functional approximations should include no less than 50% of Hartree-Fock exchange to provide accurate hyperpolarizabilities. A property-structure analysis of the azobenzene derivatives reveals that the main contribution to the first hyperpolarizability comes from the azo bond, but phenyl meso-substituents can enhance it.

Applicability of DFT functionals for evaluating the first hyperpolarizability of phenol blue in solution

The first electronic hyperpolarizability (β) of phenol blue (PB) in several solvents in a wide range of dielectric constants is investigated using the density functional theory (DFT). The reliability of various exchange-correlation functionals is assessed by a comparison to reference Møller-Plesset second-order perturbation theory (MP2) calculations. The equilibrium geometry of PB in each solvent is obtained by using the average solvent electrostatic configuration/free energy gradient method, which performs optimizations on the free energy hyper-surface by employing iteratively the sequential quantum mechanics/molecular mechanics methodology. The dependence of β on the bond length alternation (BLA) coordinate is rationalized by means of the two-level model. Within the employed exchange-correlation functionals, the LC-BLYP functional shows the best performance for describing the static and dynamic MP2 results of β, which increases as the BLA diminishes, reaching a maximum in an intermediate value of BLA. The results also illustrate the role played by the difference between the ground- and excited-state dipole moments (Δμ) in determining the hyperpolarizability behavior in solution. Particularly, in the aqueous solution case, Δμ goes to around zero when BLA is near zero, leading to an abrupt decline in the β value. The DFT results of this study, therefore, indicate a clear relationship between the first hyperpolarizability and the BLA coordinate for the PB in solution, in agreement with experiment.

Isotope-specific reactions of acetonitrile (CH3CN) with trapped, translationally cold CCl. J Chem Phys 2021;154:074305. [PMID: 33607907 DOI: 10.1063/5.0038113]

The gas-phase reaction of CCl⁺ with acetonitrile (CH₃CN) is studied using a linear Paul ion trap coupled to a time-of-flight mass spectrometer. This work builds on a previous study of the reaction of CCl⁺ with acetylene [K. J. Catani et al., J. Chem. Phys. 152, 234310 (2020)] and further explores the reactivity of CCl⁺ with organic neutral molecules. Both of the reactant species are relevant in observations and models of chemistry in the interstellar medium. Nitriles, in particular, are noted for their relevance in prebiotic chemistry and are found in the atmosphere of Titan, one of Saturn's moons. This work represents one of the first studied reactions of a halogenated carbocation with a nitrile and the first exploration of CCl⁺ with a nitrile. Reactant isotopologues are used to unambiguously assign ionic primary products from this reaction: HNCCl⁺ and C₂H₃ ⁺. Branching ratios are measured, and both primary products are determined to be equally probable. Quantum chemical and statistical reaction rate theory calculations illuminate pertinent information for interpreting the reaction data, including reaction thermodynamics and a potential energy surface for the reaction, as well as rate constants and branching ratios for the observed products. In particular, the reaction products and potential energy surface stimulate questions regarding the strength and role of the nitrile functional group, which can be further explored with more reactions of this class.

Size-, electric-field-, and frequency-dependent third-order nonlinear optical properties of hydrogenated silicon nanoclusters

We investigated the electronic properties and second hyperpolarizabilities of hydrogenated silicon nanoclusters (H-SiNCs) by using the density functional theory method. The effects of cluster size, external electric field and incident frequency on the second hyperpolarizability were also examined, respectively. We found that small H-SiNCs exhibit large second hyperpolarizability. With the increase of the number of silicon atoms in H-SiNCs, the frontier molecular orbital energy gap decreases, attributed to the enhancement of the second hyperpolarizability. Interestingly, we also found the electric-field-induced gigantic enhancement of the second hyperpolarizability for H-SiNCs due to the change of electron density distributions. In addition, our results demonstrate a significant dependence on the frequency of incident light.

Polarization response of clathrate hydrates capsulated with guest molecules

Clathrate hydrates are characterized by their water cages encapsulating various guest atoms or molecules. The polarization effect of these guest-cage complexes was studied with combined density functional theory and finite-field calculations. An addition rule was noted for these systems whose total polarizability is approximately equal to the polarizability sum of the guest and the cage. However, their distributional polarizability computed with Hirshfeld partitioning scheme indicates that the guest-cage interaction has considerable influence on their polarization response. The polarization of encapsulated guest is reduced while the polarization of water cage is enhanced. The counteraction of these two opposite effects leads to the almost unchanged total polarizability. Further analysis reveals that the reduced polarizability of encapsulated guest results from the shielding effect of water cage against the external field and the enhanced polarizability of water cage from the enhanced bonding of hydrogen bonds among water molecules. Although the charge transfer through the hydrogen bonds is rather small in the water cage, the polarization response of clathrate hydrates is sensitive to the changes of hydrogen bonding strength. The guest encapsulation strengthens the hydrogen bonding network and leads to enhanced polarizability.

Investigating the first hyperpolarizability of liquid carbon tetrachloride

Sequential QMMM calculations have been carried out to investigate the first hyperpolarizability of liquid CCl₄.

The first hyperpolarizability of nitrobenzene in benzene solutions: investigation of the effects of electron correlation within the sequential QM/MM approach

Molecular polarization due to solvation amplifies the impact of electron correlation on the first hyperpolarizability of nitrobenzene.

SCC-DFTB calculation of the static first hyperpolarizability: from gas phase molecules to functionalized surfaces

The performance of the self-consistent charge density functional tight binding (SCC-DFTB) method for calculating the first hyperpolarizability of π-conjugated compounds has been assessed with respect to results obtained with high-level ab initio methods and density functional theory (DFT). The SCC-DFTB method performs similarly or better than DFT with the PBE XC functional. Thus, if for small π-conjugated linkers SCC-DFTB can reproduce trends, for longer chains the first hyperpolarizabilities are overestimated. In the case of push-pull thiophenes, the β values are strongly overestimated, as it is also the case with the B3LYP and PBE XC functionals. On the other hand, the SCC-DFTB method closely reproduces the evolution of β in p-disubstituted benzenes as a function of the donor and acceptor groups, as estimated at the MP2 level. The reliability of SCC-DFTB to determine the bond length alternation and the dihedral angles between the aromatic rings has also been tackled, demonstrating that both are underestimated. Overall, the SCC-DFTB calculations are of the same quality as those performed with the conventional PBE XC functional on which the method was parameterized but the SCC-DFTB calculations are computationally very little demanding, and it can therefore be adopted for very large systems for screening nonlinear optical materials as well as for assessing structure-property relationships. This is illustrated with an application on the first hyperpolarizability of an indolino-oxazolidine molecular switch grafted on a SiO2 surface. This has enabled to pinpoint (i) the effect of the surface on the donor/acceptor character of the linking substituent, (ii) the impact of molecular orientation, (iii) the role of a spacer between the π-conjugated switch and the surface, (iv) the global effect of the surface on the β contrast, and also (v) the fact that the molecular switches can maintain this contrast when adsorbed.

Computational study on redox-switchable second-order nonlinear optical properties of ferrocene-tetrathiafulvalene hybrid

Redox-switchable second-order nonlinear optical (NLO) responses of a series of ferrocene-tetrathiafulvalene (Fc–TTF) hybrids have been studied based on density functional theory calculations.

New acceptor-bridge-donor strategy for enhancing NLO response with long-range excess electron transfer from the NH2...M/M3O donor (M = Li, Na, K) to inside the electron hole cage C20F19 acceptor through the unusual σ chain bridge (CH2)4

Using the strong electron hole cage C20F19 acceptor, the NH2...M/M3O (M = Li, Na, and K) complicated donors with excess electron, and the unusual σ chain (CH2)4 bridge, we construct a new kind of electride molecular salt e(-)@C20F19-(CH2)4-NH2...M(+)/M3O(+) (M = Li, Na, and K) with excess electron anion inside the hole cage (to be encapsulated excess electron-hole pair) serving as a new A-B-D strategy for enhancing nonlinear optical (NLO) response. An interesting push-pull mechanism of excess electron generation and its long-range transfer is exhibited. The excess electron is pushed out from the (super)alkali atom M/M3O by the lone pair of NH2 in the donor and further pulled inside the hole cage C20F19 acceptor through the efficient long σ chain (CH2)4 bridge. Owing to the long-range electron transfer, the new designed electride molecular salts with the excess electron-hole pair exhibit large NLO response. For the e(-)@C20F19-(CH2)4-NH2...Na(+), its large first hyperpolarizability (β0) reaches up to 9.5 × 10(6) au, which is about 2.4 × 10(4) times the 400 au for the relative e(-)@C20F20...Na(+) without the extended chain (CH2)4-NH2. It is shown that the new strategy is considerably efficient in enhancing the NLO response for the salts. In addition, the effects of different bridges and alkali atomic number on β0 are also exhibited. Further, three modulating factors are found for enhancing NLO response. They are the σ chain bridge, bridge-end group with lone pair, and (super)alkali atom. The new knowledge may be significant for designing new NLO materials and electronic devices with electrons inside the cages. They may also be the basis of establishing potential organic chemistry with electron-hole pair.

Electric dipole (hyper)polarizabilities of spatially confined LiH molecule

In this study we report on the electronic contributions to the linear and nonlinear static electronic electric dipole properties, namely the dipole moment (μ), the polarizability (α), and the first-hyperpolarizability (β), of spatially confined LiH molecule in its ground X (1)Σ(+) state. The finite-field technique is applied to estimate the corresponding energy and dipole moment derivatives with respect to external electric field. Various forms of confining potential, of either spherical or cylindrical symmetry, are included in the Hamiltonian in the form of one-electron operator. The computations are performed at several levels of approximation including the coupled-cluster methods as well as multi-configurational (full configuration interaction) and explicitly correlated Gaussian wavefunctions. The performance of Kohn-Sham density functional theory for the selected exchange-correlation functionals is also discussed. In general, the orbital compression effects lead to a substantial reduction in all the studied properties regardless of the symmetry of confining potential, however, the rate of this reduction varies depending on the type of applied potential. Only in the case of dipole moment under a cylindrical confinement a gradual increase of its magnitude is observed.