Chirality-Induced Spin Selectivity: Analysis of Density Functional Theory Calculations.

Chirality-induced spin selectivity (CISS), which was demonstrated in several molecular and material systems, has drawn much interest recently. The phenomenon, described in electron transport by the difference in the transport rate of electrons of opposite spins through a chiral system, is however not fully understood. Herein, we employed density functional theory in conjunction with spin-orbit coupling to evaluate the percent spin-polarization in a device setup with finite electrodes at zero bias, using an electron transport program developed in-house. To study the interface effects and the level of theory considered, we investigated a helical oligopeptide chain, an intrinsically chiral gold cluster, and a helicene model system that was previously studied (Zöllner et al. J. Chem. Theory Comput. 2020, 16, 7357-7371). We find that the magnitude of the spin-polarization depends on the chiral system-electrode interface that is modeled by varying the interface boundary between the system's regions, on the method of calculating spin-orbit coupling, and on the exchange-correlation functional, e.g., the amount of exact exchange in the hybrid functionals. In addition, to assess the effects of bias, we employ the nonequilibrium Green's function formalism in the Quantum Atomistix Toolkit program, showing that the spin-flip terms could be important in calculating the CISS effect. Although understanding CISS in comparison to experiment is still not resolved, our study provides intrinsic responses from first-principles calculations.

Theoretical Investigation of the Electronic Spectra of Cadmium Chalcogenide 2D Nanoplatelets.

Although colloidal cadmium chalcogenide 2D nanoplatelets (NPLs) have recently demonstrated strongly enhanced one- and two-photon absorption (OPA, TPA) spectra, an understanding of the effects of quantum confinement in the lateral and vertical (thickness) dimensions is mostly lacking. In this work, we investigate theoretically CdS and CdSe NPLs passivated with formate and acetate ligands with thicknesses of two and three monolayers (MLs) and different lateral dimensions. Initial structures for CdS nanoplatelets were obtained using our recently developed deep neural network potential, and the low-energy geometries were subsequently optimized using density functional theory (DFT). Linear- and nonlinear-response calculations using time-dependent DFT (TDDFT) and the simplified Tamm-Dancoff approximation (sTDA) demonstrated good agreement between measured spectra and calculated TDDFT and sTDA spectra for 2 and 3 ML NPLs. The OPA red-shifts from 2 to 3 ML NPLs can be attributed to the electron delocalization in the lateral and vertical directions. TPA responses for CdS and CdSe NPLs were found to be dominated by weakly absorbing and forbidden OPA states.

Calculated linear and nonlinear optical absorption spectra of phosphine-ligated gold clusters.

Although prediction of optical excitations of ligated gold clusters by time-dependent density functional theory (TDDFT) is relatively well-established, limitations still exist, for example in the choice of the exchange-correlation functional. In aiming to improve on the accuracy of the calculated linear absorption, we report a theoretical study on phosphine-ligated gold clusters, specifically Au9(PR3)83+ and Au8(PR3)72+ characterized by highly resolved UV/Vis spectra, using mass-selective electronic absorption photofragmentation spectroscopy (A. Cirri, H. M. Hernández and C. J. Johnson, J. Phys. Chem. A, 2020, 124, 1467-1479, and references therein). The optical absorption spectra of the Au9(PR3)83+ and Au8(PR3)72+ clusters were calculated using TDDFT and the many-body GW (G-Green's function, and W-screened Coulomb interaction)-BSE (Bethe Salpeter Equation) method, and compared to the experimental measurements. The evGW-BSE results demonstrated fair agreement with the experimental data, comparable to the TDDFT results, but with less dependence on the reference exchange-correlation functional. Experimentally observed ligand-effects in these materials were reproduced in our calculations as well. Finally, to assess the utility of the materials for nonlinear optical absorption, a theoretical evaluation of two-photon absorption cross-sections is included.

Theoretical analysis of structures and electronic spectra of molecular colloidal cadmium sulfide clusters and nanoplatelets.

In the present study, we systematically examine structures and absorption spectra for CdS nanoplatelets (NPLs) with thicknesses of two and three monolayers (2 MLs and 3 MLs) and extended lateral dimensions. These nanoplatelet model systems, passivated with formate and acetate ligands, are used to analyze the effects of quantum confinement in the lateral dimension within an extended monolayer and the effects of thickness when changing from two to three monolayers. Based on the computed cubic structures using density functional theory (DFT), we found good agreement between observed and time-dependent DFT-calculated spectra, revealing little ligand participation to influence the color and intensity of low-energy absorption bands as the structures are laterally extended to eight and seven monolayers for 2-ML and 3-ML systems, respectively. The spectral redshift for 3-ML CdS NPLs is attributed to the electron delocalization due to expansion of the nanoplatelet in the lateral and vertical directions.

Systematic Study of the Properties of CdS Clusters with Carboxylate Ligands Using a Deep Neural Network Potential Developed with Data from Density Functional Theory Calculations.

Although structures of the inorganic core of CdS atomically precise quantum dots were reported, characterizing the nature of the metal-carboxylate coordination in these materials remains a challenge due to the large number of possible isomers. The computational cost imposed by first-principles methods is prohibitive for such a configurational search, and empirical potentials are not available. In this work, we applied deep neural network algorithms to train a potential for CdS clusters with carboxylate ligands using a database of energies and gradients obtained from density functional theory calculations. The derived potential provided energies and gradients based on a set of reference structures. Our trained potential was then used to accelerate genetic algorithm and molecular dynamics simulations searches of low-energy structures, which in turn, were used to compute the X-ray diffraction and electronic absorption spectra. Our results for CdS clusters with carboxylate ligands, analyzed and compared with experimental findings, demonstrated that the structure of a cluster whose properties agree better with experiment may deviate from the one previously assumed.

Theoretical Prediction of Optical Absorption and Emission in Thiolated Gold Clusters.

Although the photoluminescence of gold clusters has been extensively studied so far, there are still questions on the origin of the emission in these materials. In this work, we report time-dependent density functional theory calculations on the absorption and emission spectra of the well-studied Au25(SR)18- cluster, the lowest energy isomer of the Au38(SR)24 cluster, and five isomers of the Au22(SR)18 cluster. Good agreement between the calculated and measured absorption spectra, as well as with the lowest-energy emission values for these clusters, was demonstrated, verifying the accuracy of the theoretical methods employed. Our results for Au25(SR)18- explain a newly observed feature in the absorption peak, also rationalizing the optical response in terms of the superatom model. The analysis of the absorption and emission characteristics of the Au25(SR)18- and Au38(SR)24 clusters provides an estimate of the spectral regions, where fluorescence or phosphorescence is predicted to occur. Interestingly, we find that for Au22(SR)18, one of the five proposed structures could be present at a significant concentration in the sample, even though it is not the lowest in energy structure, which can be explained, in part, by solvent effects.

Systematic Study of Structure, Stability, and Electronic Absorption of Tetrahedral CdSe Clusters with Carboxylate and Amine Ligands.

In this work, we carried out a systematic investigation to assess the effects of ligands on the structure, stability, and absorption spectra of ultrasmall CdSe tetrahedral quantum dots, where the cores of small tetrahedral quantum dots have been postulated to be stabilized by amine and carboxylate ligands. We found that amine and carboxylate ligands form extensive hydrogen bonding networks, which provide thermodynamic stability to the clusters. On the basis of the optimized structures, good agreement between observed and computed spectra was obtained. The ligands were also found to have a large influence on the color and intensity of the electronic absorption spectra, particularly for the small clusters, which were previously monitored with in situ UV-visible absorbance spectroscopy. Our work provides an understanding of the effect of ligands that influence thermodynamic stability and electronic absorption of ultrasmall quantum dots, thus potentially motivating further experimental exploration.

Theoretical Analysis of Optical Absorption and Emission in Mixed Noble Metal Nanoclusters.

In this work, we studied theoretically two hybrid gold-silver clusters, which were reported to have dual-band emission, using density functional theory (DFT) and linear and quadratic response time-dependent DFT (TDDFT). Hybrid functionals were found to successfully predict absorption and emission, although explanation of the NIR emission from the larger cluster (cluster 1) requires significant vibrational excitation in the final state. For the smaller cluster (cluster 2), the Δ H(0-0) value calculated for the T1 → S0 transition, using the PBE0 functional, is in good agreement with the measured NIR emission, and the calculated T2 → S0 value is in fair agreement with the measured visible emission. The calculated T1 → S0 phosphorescence Δ H(0-0) for cluster 1 is close to the measured visible emission energy. In order for the calculated phosphorescence for cluster 1 to agree with the intense NIR emission reported experimentally, the vibrational energy of the final state (S0) is required to be about 0.7 eV greater than the zero-point vibrational energy.

Calculations of One- and Two-Photon Absorption Spectra for Molecular Metal Chalcogenide Clusters with Electron-Acceptor Ligands.

We present calculated one- and two-photon absorption (OPA, TPA) spectra for molecular neutral, cation, and anion cadmium chalcogenide nonstoichiometric clusters [CdnE'm'(ER)m, E = S and Se, R = hydrogen, methyl, phenyl, para-nitrophenyl, para-cyanophenyl], ranging from less than 1 nm to more than 2 nm in size with well-defined structures. A systematic treatment of the clusters is carried out to assess the effects of size and ligand on their linear and nonlinear optical properties. Ligands and cluster size were found to have a large influence on the color and intensity of the electronic absorption spectra. TPA cross sections were found to increase linearly with cluster size. Electron-accepting ligands were also found to induce linear enhancement in TPA cross sections. Blue shifts of TPA maxima were observed for the first band with reduced molecular size. The effects of phenyl, para-nitrophenyl, and para-cyanophenyl substitutions, as well as changes in the chalcogenide atom, have been analyzed in detail.

A Theoretical Investigation of the Structure and Optical Properties of a Silver Cluster in Solid Form and in Solution.

Using density functional theory (DFT) and linear and quadratic response time-dependent DFT, we investigated the structure and optical properties of a silver sulfide cluster with the interesting property of dual emission that was observed when in crystal form but not in solution. Since the dual fluorescence is observed only in the crystal, a supposition of stabilization of a higher-energy excited state by an excimer-like complex was analyzed by calculations for a cluster dimer, formed through π-stacking of aromatic groups bonded to the sulfur atoms. However, because of the complexity of the system, a simple one-dimensional method for dimer optimization, which works moderately well in predicting the red-shifted fluorescence compared to its absorption in a naphthalene dimer, predicts only partially the red shift for the emission energy. Interestingly, calculations of the two-photon absorption (TPA) cross-section on the optimized isolated cluster as well as the crystal structure geometry indicate significant off-resonance TPA. While some materials have significantly larger TPA cross-sections, such a TPA cross-section off-resonance could be useful. The high density of states in the dimer system results in a higher probability for significant resonance enhancement and thus much larger TPA cross-sections.

Linear and Nonlinear Optical Response in Silver Nanoclusters: Insight from a Computational Investigation.

We report a density functional theory (DFT) and time-dependent DFT (TDDFT) investigation of the thiolated silver nanoclusters [Ag44(SR)30](4-), Ag14(SR)12(PR'3)8, Ag31(SG)19, Ag32(SG)19, and Ag15(SG)11, which were synthesized and for which one-photon absorption (OPA) characterization is available. Our computational investigation based on careful examination of the exchange-correlation functional used in DFT geometry optimization and for the linear optical properties predictions by TDDFT, demonstrated good agreement with the measured linear absorption spectra, however dependent on the applied functional. Following the benchmarking, we evaluated the two-photon absorption (TPA) response using TDDFT, noting that accurate prediction of OPA is important for suppositions on the spectral range for TPA enhancement because of the sensitivity to the excitation energies. Although the TPA cross-section results are complicated by resonance effects and quantifying TPA cross sections for these systems is difficult, our results indicate that the nanoclusters Ag15 and Ag31/32 are likely to have large TPA cross sections. The spherical symmetry of the Ag44 and Ag14 nanoclusters leads to applicability of superatom theory, while it is not as useful for the more oblate geometries of the Ag15 and Ag31/32 systems.

Theoretical analysis of structures and electronic spectra in molecular cadmium chalcogenide clusters.

We present calculated structural and optical properties of molecular cadmium chalcogenide nonstoichiometric clusters with a size range of less than 1 nm to more than 2 nm with well-defined chemical compositions and structures in comparison to experimental characterization and previous theoretical work. A unified treatment of these clusters to obtain a fundamental understanding of the size, ligand, and solvation effects on their optical properties has not been heretofore presented. The clusters belong to three topological classes, specifically supertetrahedral (Tn), penta-supertetrahedral (Pn), and capped supertetrahedral (Cn), where n is the number of metal layers in each cluster. The tetrahedrally shaped Tn clusters examined in this work are Cd(ER)4(2-) (T1), Cd4(ER)10(2-) (T2), and Cd10E4 (')(ER)16(4-) (T3), where R is an organic group, E and E' are chalcogen atoms (sulfur or selenium). The first member of the Pn series considered is M8E'(ER)16(2-). For the Cn series, we consider the first three members, M17E4 (')(ER)28(2-), M32E14 (')(ER)36L4, and M54E32 (')(ER)48L4(4-) (L = neutral ligand). Mixed ligand clusters with capping ER groups replaced by halogen or neutral ligands were also considered. Ligands and solvent were found to have a large influence on the color and intensity of the electronic absorption spectra of small clusters. Their effects are generally reduced with increasing cluster sizes. Blueshifts were observed for the first electronic transition with reduced size for both cadmium sulfide and cadmium selenide series. Due to weakly absorbing and forbidden transitions underlying the one-photon spectra, more care is needed in interpreting the quantum confinement from the clusters' lowest-energy absorption bands.

Density functional theory based generalized effective fragment potential method.

We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.

Analysis of nonlinear optical properties in donor-acceptor materials.

Time-dependent density functional theory has been used to calculate nonlinear optical (NLO) properties, including the first and second hyperpolarizabilities as well as the two-photon absorption cross-section, for the donor-acceptor molecules p-nitroaniline and dimethylamino nitrostilbene, and for respective materials attached to a gold dimer. The CAMB3LYP, B3LYP, PBE0, and PBE exchange-correlation functionals all had fair but variable performance when compared to higher-level theory and to experiment. The CAMB3LYP functional had the best performance on these compounds of the functionals tested. However, our comprehensive analysis has shown that quantitative prediction of hyperpolarizabilities is still a challenge, hampered by inadequate functionals, basis sets, and solvation models, requiring further experimental characterization. Attachment of the Au2S group to molecules already known for their relatively large NLO properties was found to further enhance the response. While our calculations show a modest enhancement for the first hyperpolarizability, the enhancement of the second hyperpolarizability is predicted to be more than an order of magnitude.

Computational Prediction of Structures and Optical Excitations for Nanoscale Ultrasmall ZnS and CdSe Clusters.

Small semiconductor nanoclusters are important for understanding the initial formation and growth of quantum dots and also for application, for example in the tunability provided by size. However, electronic structures and effects of capping ligands have not been systematically characterized. Thus, ground and excited state calculations using coupled-cluster methods were carried out to provide benchmarks for evaluating the applicability of density functional theory (DFT) and time-dependent DFT (TDDFT) with different functionals for the ground and excited states, respectively. Our computed data suggests that the popular B3LYP functional does not deliver optimal results for the ground and excited state. While the PBE0 functional was found to provide a good description for both the ground and excited states for small bare (ZnS)n and bare and ligated (CdSe)n clusters, the results for the hydrated (ZnS)n clusters were found to deteriorate significantly. However, the errors appear to decrease with increasing cluster size. Excitation energies obtained with the long-range hybrid CAM-B3LYP and CA-B3LYP were found to provide more consistent results for both anhydrous and hydrated (ZnS)n clusters. However, their performance in spectral predictions for larger clusters requires further study. Using PBE0, electronic structures of the ground and excited states for (ZnS)n and (CdSe)n up to n = 37 using DFT and TDDFT, respectively, were re-examined. With the exception of the cage-core (ZnS)13, (CdSe)13, and (CdSe)14, small (ZnS)n and (CdSe)n are predicted to be spheroids and tubular structures (6, 8-12, 15-19) with squares and hexagons, similar to the structures of carbon single-wall nanotubes. Wurtzite (n = 23-27, 36, 37) and cage-core (n = 29-35) structures are energetically more favorable for larger clusters. We find that water and amines increase the intensities and blue shift the excitations of bare clusters. One photon absorption spectra predicted by TDDFT with the PCM solvation model for (CdSe-methylamine)13 and the larger ligated (CdSe)33 are consistent with the experimental spectra.

Alternative Mechanisms in Hydrogen Production by Aluminum Anion Clusters.

Possible mechanisms for the reaction of aluminum anion clusters with water have been studied theoretically using density functional theory for four different size clusters. Our results confirm the previously found (Reber et al. J. Phys. Chem. A2010, 114, 6071) importance of Lewis-acid and Lewis-base sites on the cluster in the size specificity of the reactivity. However, alternative viable mechanisms have been found using both Langmuir-Hinshelwood and Eley-Rideal kinetics. Grotthuss-like mechanisms appear to be the most energetically favorable. We show that while the superatom theory successfully predicts reactivity of smaller clusters, it is less useful for the larger clusters.

The performance and relationship among range-separated schemes for density functional theory.

The performance and relationship among different range-separated (RS) hybrid functional schemes are examined using the Coulomb-attenuating method (CAM) with different values for the fractions of exact Hartree-Fock (HF) exchange (α), long-range HF (ß), and a range-separation parameter (µ), where the cases of α + ß = 1 and α + ß = 0 were designated as CA and CA0, respectively. Attenuated PBE exchange-correlation functionals with α = 0.20 and µ = 0.20 (CA-PBE) and α = 0.25 and µ = 0.11 (CA0-PBE) are closely related to the LRC-ωPBEh and HSE functionals, respectively. Time-dependent density functional theory calculations were carried out for a number of classes of molecules with varying degrees of charge-transfer (CT) character to provide an assessment of the accuracy of excitation energies from the CA functionals and a number of other functionals with different exchange hole models. Functionals that provided reasonable estimates for local and short-range CT transitions were found to give large errors for long-range CT excitations. In contrast, functionals that afforded accurate long-range CT excitation energies significantly overestimated energies for short-range CT and local transitions. The effects of exchange hole models and parameters developed for RS functionals for CT excitations were analyzed in detail. The comparative analysis across compound classes provides a useful benchmark for CT excitations.

Calculation of One- and Two-Photon Absorption Spectra of Thiolated Gold Nanoclusters using Time-Dependent Density Functional Theory.

The one- (OPA) and two-photon (TPA) absorption spectra have been calculated for a gold dimer, for a monothiolated gold dimer anion, for a thiolated gold cluster [Au25(SH)18](-1), whose structure has been determined, and for a proposed cluster [Au12(SR)9](+1) using time-dependent density functional theory (TDDFT). Geometry optimization with different exchange-correlation (X-C) functionals yielded small differences which had significant consequences in the spectra calculations. The calculated excitation energies of Au25(SH)18(-1) are in excellent agreement with experiment when the local density approximation Xα-optimized geometry is used with the B3LYP X-C functional. The CAMB3LYP and mCAM functionals yielded OPA results in good agreement with experiment for the dimer systems and the larger clusters. The super-atom theory was useful in analyzing the electronic transitions in the larger clusters. TPA was dominated by resonance effects, and the calculated cross-sections displayed a strong X-C functional dependence.

One- and two-photon spectra of platinum acetylide chromophores: a TDDFT study.

We report one- (OPA) and two-photon absorption (TPA) excitation energies and cross-sections for a series of platinum acetylides using time-dependent density functional theory. Because of the facile rotations of the trimethylphosphinyl and phenylene groups, we apply a Boltzmann-weighted average over thermally accessible conformations to obtain the final spectra, resulting in better agreement with experimental observations. We examine various basis sets and functionals to evaluate their performance in the gas-phase and in solution. Effects of donor and acceptor groups on the OPA and TPA resonances and intensities are also discussed.

Calculation of One-Photon and Two-Photon Absorption Spectra of Porphyrins Using Time-Dependent Density Functional Theory.

Time-dependent density functional theory has been used to calculate the one-photon and two-photon absorption spectra of free-base porphyrin, a substituted zinc porphyrin, and a zinc porphyrin dimer, in order to assess the validity of the method to reproduce the large increase in the two-photon absorption (TPA) cross-section for the dimer. Three hybrid functionals with varying amounts of exact exchange were tested, and the calculated one-photon absorption spectra for each of the molecular systems were shown to be in qualitative agreement with the measured spectra. All three functionals predict a large enhancement in the TPA cross-section for the dimer relative to the monomer, in agreement with experimental results. However, because of the sensitivity of the resonance enhancement factor to small differences in the relevant state energies, quantitative prediction of the TPA cross-section by this method is still a challenge.