Convergence of Time-Derivative Nonadiabatic Couplings in Plane-Wave DFT Calculations.

Accurate prediction of charge carrier relaxation rates is essential to design molecules and materials with the desired photochemical properties for applications like photocatalysis and solar energy conversion. Nonadiabatic molecular dynamics allows one to simulate the relaxation process of excited charge carriers. Plane-wave density functional theory (DFT) calculations make the time-derivative nonadiabatic couplings (TNACs) simple to compute because the basis is independent of the atomic positions. However, the effect of the kinetic energy cutoff for the plane-wave basis on the accuracy of the dynamics has not been studied. Here, we examine the effect of the kinetic energy cutoff on the TNACs and decay time scales for the prototypical model system of tetracene. These calculations show that the choice of kinetic energy cutoff can change the relaxation time by up to 30%. The relaxation times of states that have small TNACs to other states or are far from degenerate are more sensitive to the kinetic energy cutoff than those of states with large TNACs or near degeneracies. A kinetic energy cutoff of 60 Ry is sufficient for all states to reach semiquantitative agreement (absolute error <10%) with the decay times of our 110 Ry reference data, and a cutoff of 80 Ry is required for all states to reach quantitative agreement (absolute error <2%).

Bonding and Acidity of the Formal Hydride in the Prototypical Au9 (PPh3 )8 H2+ Nanocluster.

The role of hydrogen atoms as surface ligands on metal nanoclusters is of profound importance but remains difficult to directly study. While hydrogen atoms often appear to be incorporated formally as hydrides, evidence suggests that they donate electrons to the cluster's delocalized superatomic orbitals and may consequently behave as acidic protons that play key roles in synthetic or catalytic mechanisms. Here we directly test this assertion for the prototypical Au9 (PPh3 )8 H2+ nanocluster, formed by addition of a hydride to the well-characterized Au9 (PPh3 )8 3+ . Using gas-phase infrared spectroscopy, we were able to unambiguously isolate Au9 (PPh3 )8 H2+ and Au9 (PPh3 )8 D2+ , revealing an Au-H stretching mode at 1528 cm-1 that shifts to 1038 cm-1 upon deuteration. This shift is greater than the maximum expected for a typical harmonic potential, suggesting a potential governing cluster-H bonding that has some square-well character consistent with the hydrogen nucleus behaving as a metal atom in the cluster core. Complexing this cluster with very weak bases reveals a redshift of 37 cm-1 in the Au-H vibration, consistent with those typically seen for moderately acidic groups in gas phase molecules and providing an estimate of the acidity of Au9 (PPh3 )8 H2+ , at least with regard to its surface reactivity.

Parametrization of the PM7 Semiempirical Quantum Mechanical Method for Silver Nanoclusters.

Semiempirical quantum mechanical methods (SEQMs) are widely used in computational chemistry because of their low computational cost, but their accuracy depends on the quality of the parameters. The neglect of diatomic differential overlap method PM7 is among the few SEQMs that contain parameters for Ag, but the experimental reference data was insufficient to obtain reliable parameters in the original parametrization. In this work, we reparametrize the PM7 parameters for Ag to accurately reproduce the ground-state potential energy surfaces of Ag clusters. Since little experimental data is available, we use reference data obtained from the ab initio method CCSD(T). The resulting parameters significantly reduce the errors in binding energies, energies required to displace clusters along their normal modes, and relative energies of isomers compared to the default PM7 Ag parameters.

Evolution of plasmon-like excited states in silver nanowires and nanorods.

Silver nanowires and nanorods are useful prototypical systems to study the emergence of plasmons within a quantum mechanical context because their high aspect ratios enable plasmons to emerge in smaller systems than for roughly spherical nanoclusters. Here, we quantify the plasmon-like character of the excited states of silver nanorods and nanowires based on three nearly orthogonal criteria: (1) collectivity, (2) dipole additivity, and (3) superatomic character. Based on these three criteria, we classify the excited states as plasmon-like, collective, single-particle, interband, or as intermediate between these categories. We show that linear nanowires have a longitudinal absorption peak that has single-particle character and a transverse absorption peak that evolves from a single-particle to plasmon-like to a mix of plasmon-like and interband with increasing length. Increasing the width tends to increase the plasmon-like character of the longitudinal excited state. In contrast, increasing the nanorod width tends to decrease the length at which interband transitions start mixing significantly into the transverse plasmon-like excited states.

Plasmons: untangling the classical, experimental, and quantum mechanical definitions.

Plasmons have been widely studied over the past several decades because of their ability to strongly absorb light and localize its electric field on the nanoscale, leading to applications in spectroscopy, biosensing, and solar energy storage. In a classical electrodynamics framework, a plasmon is defined as a collective, coherent oscillation of the conduction electrons of the material. In recent years, it has been shown experimentally that noble metal nanoclusters as small as a few nm can support plasmons. This work has led to numerous attempts to identify plasmons from a quantum mechanical perspective, including many overlapping and sometimes conflicting criteria for plasmons. Here, we shed light on the definitions of plasmons. We start with a brief overview of the well-established classical electrodynamics definition of a plasmon. We then turn to the experimental features used to determine whether a particular system is plasmonic, connecting the experimental results to the corresponding features of the classical electrodynamics description. The core of this article explains the many quantum mechanical criteria for plasmons. We explore the common features that these criteria share and explain how these features relate to the classical electrodynamics and experimental definitions. This comparison shows where more work is needed to expand and refine the quantum mechanical definitions of plasmons.

Hydride- and halide-substituted Au9(PH3)83+ nanoclusters: similar absorption spectra disguise distinct geometries and electronic structures.

Ligands dramatically affect the electronic structure of gold nanoclusters (NCs) and provide a useful handle to tune the properties required for nanomaterials that have high performance for important functions like catalysis. Recently, questions have arisen about the nature of the interactions of hydride and halide ligands with Au NCs: hydride and halide ligands have similar effects on the absorption spectra of Au9 NCs, which suggested that the interactions of the two classes of ligands with the Au core may be similar. Here, we elucidate the interactions of halide and hydride ligands with phosphine-protected gold clusters via theoretical investigations. The computed absorption spectra using time-dependent density functional theory are in reasonable agreement with the experimental spectra, confirming that the computational methods are capturing the ligand-metal interactions accurately. Despite the similarities in the absorption spectra, the hydride and halide ligands have distinct geometric and electronic effects. The hydride ligand behaves as a metal dopant and contributes its two electrons to the number of superatomic electrons, while the halides act as electron-withdrawing ligands and do not change the number of superatomic electrons. Clarifying the binding modes of these ligands will aid in future efforts to use ligand derivatization as a powerful tool to rationally design Au NCs for use in functional materials.

A new release of MOPAC incorporating the INDO/S semiempirical model with CI excited states.

The semiempirical INDO/S Hamiltonian is incorporated into a new release of MOPAC2016. The MOPAC2016 software package has long been at the forefront of semiempirical quantum chemical methods (SEQMs) for small molecules, proteins, and solids and until this release has included only NDDO-type SEQMs. The new code enables the calculation of excited states using the INDO/S Hamiltonian combined with a configuration interaction (CI) approach using single excitations (CIS), single and double excitations (CISD), or multiple reference determinants (MRCI) where reference determinants are generated using a complete active space (CAS) approach. The capacity to perform excited-state calculations beyond the CIS level makes INDO/CI one of the few low-cost computational methods capable of accurately modeling states with substantial double-excitation character. Solvent corrections to the ground-state and excited-state energies can be computed using the COSMO implicit solvent model, incorporating state-specific corrections to the excited states based on the solvent refractive index. This code produces physically reasonable electronic structures, absorption spectra, and solvatochromic shifts at low computational costs for systems up to hundreds of atoms, and for both organic molecules and metal clusters.

Molecular engineering of organic semiconductors enables noble metal-comparable SERS enhancement and sensitivity.

Nanostructured molecular semiconductor films are promising Surface-Enhanced Raman Spectroscopy (SERS) platforms for both fundamental and technological research. Here, we report that a nanostructured film of the small molecule DFP-4T, consisting of a fully π-conjugated diperfluorophenyl-substituted quaterthiophene structure, demonstrates a very large Raman enhancement factor (>105) and a low limit of detection (10-9 M) for the methylene blue probe molecule. This data is comparable to those reported for the best inorganic semiconductor- and even intrinsic plasmonic metal-based SERS platforms. Photoluminescence spectroscopy and computational analysis suggest that both charge-transfer energy and effective molecular interactions, leading to a small but non-zero oscillator strength in the charge-transfer state between the organic semiconductor film and the analyte molecule, are required to achieve large SERS enhancement factors and high molecular sensitivities in these systems. Our results provide not only a considerable experimental advancement in organic SERS figure-of-merits but also a guidance for the molecular design of more sensitive SERS systems.

Benchmarking Semiempirical Methods To Compute Electrochemical Formal Potentials.

Computational methods to predict and tune electrochemical redox potentials are important for the development of energy technologies. Here, we benchmark several semiempirical models to compute reduction potentials of organic molecules, comparing approaches based on (1) energy differences between the S0 and one-electron-reduced D0 states of the isolated molecules and (2) an orbital energy shift approach based on tuning the charge-transfer triplet energy of the Ag20-molecule complex; the second model enables explicit modeling of electrode-molecule interactions. For molecules in solution, the two models yield nearly identical results. Both PM7 and PM6 predict formal potentials with only a slight loss of accuracy compared to standard density functional theory models, and the results are robust across several choices of geometries and implicit solvent models. PM6 and PM7 show dramatically improved accuracy over older semiempirical Hamiltonians (MNDO, AM1, PM3, and INDO/S). However, our recently developed INDO parameters model the electronic properties of our Ag20 model electrode much more accurately than does PM7. These results demonstrate the need for further development of semiempirical models to accurately model molecules on surfaces.

Bias-Dependent Chemical Enhancement and Nonclassical Stark Effect in Tip-Enhanced Raman Spectromicroscopy of CO-Terminated Ag Tips.

Tip-enhanced Raman spectromicroscopy (TERS) with CO-terminated plasmonic tips can probe angstrom-scale features of molecules on surfaces. The development of this technique requires understanding of how chemical environments affect the CO vibrational frequency and TERS intensity. At the scanning tunneling microscope junction of a CO-terminated Ag tip, we show that rather than the classical vibrational Stark effect, the large bias dependence of the CO frequency shift is due to ground-state charge transfer from the Ag tip into the CO π* orbital softening the C-O bond at more positive biases. The associated increase in Raman intensity is attributed to a bias-dependent chemical enhancement effect, where a positive bias tunes a charge-transfer excited state close to resonance with the Ag plasmon. This change in Raman intensity is contrary to what would be expected based on changes in the tilt angle of the CO molecule with bias, demonstrating that the Raman intensity is dominated by electronic rather than geometric effects.

Theoretical modeling of voltage effects and the chemical mechanism in surface-enhanced Raman scattering.

Theoretical approaches can provide insight into the mechanisms and magnitudes of electromagnetic and chemical effects in surface-enhanced Raman scattering (SERS), properties that are not readily available experimentally. Here, we model the SERS spectra of two geometries of the prototypical Ag20-pyridine cluster using a semiempirical INDO/SCI approach that allows a straightforward decomposition of the enhancement factors at each wavelength into electromagnetic and chemical terms, with proper treatment of resonant charge-transfer contributions to the enhancement. The method also enables us to determine the dependence of the enhancement on the electrochemical potential. We show that the electromagnetic enhancements for the Ag20 cluster are <10 far from resonance but can increase to 102 to 103 on resonance with plasmon excitation in the cluster. The decomposition also shows that for the systems studied here, the chemical enhancements are primarily due to resonance with excited states with significant charge-transfer character. This term is typically <10 but can be >102 at electrochemical potentials where the charge-transfer excited states are resonant with the incoming light, leading to total enhancements of >104.

Nanostructured organic semiconductor films for molecular detection with surface-enhanced Raman spectroscopy.

π-Conjugated organic semiconductors have been explored in several optoelectronic devices, yet their use in molecular detection as surface-enhanced Raman spectroscopy (SERS)-active platforms is unknown. Herein, we demonstrate that SERS-active, superhydrophobic and ivy-like nanostructured films of a molecular semiconductor, α,ω-diperfluorohexylquaterthiophene (DFH-4T), can be easily fabricated by vapour deposition. DFH-4T films without any additional plasmonic layer exhibit unprecedented Raman signal enhancements up to 3.4 × 103 for the probe molecule methylene blue. The combination of quantum mechanical computations, comparative experiments with a fluorocarbon-free α,ω-dihexylquaterthiophene (DH-4T), and thin-film microstructural analysis demonstrates the fundamental roles of the π-conjugated core fluorocarbon substitution and the unique DFH-4T film morphology governing the SERS response. Furthermore, Raman signal enhancements up to ∼1010 and sub-zeptomole (<10-21 mole) analyte detection were accomplished by coating the DFH-4T films with a thin gold layer. Our results offer important guidance for the molecular design of SERS-active organic semiconductors and easily fabricable SERS platforms for ultrasensitive trace analysis.

Semiempirical modeling of electrochemical charge transfer.

Nanoelectrochemical experiments using detection based on tip enhanced Raman spectroscopy (TERS) show a broad distribution of single-molecule formal potentials E°' for large π-conjugated molecules; theoretical studies are needed to understand the origins of this distribution. In this paper, we present a theoretical approach to determine E°' for electrochemical reactions involving a single molecule interacting with an electrode represented as a metal nanocluster and apply this method to the Ag20-pyridine system. The theory is based on the semiempirical INDO electronic structure approach, together with the COSMO solvation model and an approach for tuning the Fermi energy, in which the silver atomic orbital energies are varied until the ground singlet state of Ag20-pyridine matches the lowest triplet energy, corresponding to electron transfer from the metal cluster to pyridine. Based on this theory, we find that the variation of E°' with the structure of the Ag20-pyridine system is only weakly correlated with changes in either the ground-state interaction energy or the charge-transfer excited-state energies at zero applied potential, which shows the importance of calculations that include an applied potential in determining the variation of formal potential with geometry. Factors which determine E°' include wavefunction overlap for geometries when pyridine is close to the surface, and electrostatics when the molecule-cluster separation is large.

Implementation of INDO/SCI with COSMO Implicit Solvation and Benchmarking for Solvatochromic Shifts.

Accurate and rapid quantum mechanical prediction of solvatochromic shifts, particularly in systems where charge transfer plays a significant role, is important for many aspects of molecular and material design. Although the semiempirical INDO/SCI approach is computationally efficient and performs well for charge-transfer states, the availability of implicit solvent approaches has been limited. Here, we implement the COSMO solvent model with a perturbative state-specific correction to the excited-state energies with the INDO/SCI method. We show that for a series of prototypical π-conjugated molecules, our newly implemented INDO/SCI/COSMO model yields more accurate absorption energies and comparably accurate solvatochromic shifts to those computed using TD-ωB97XD and CIS with COSMO solvation at a substantially lower computational cost.

Benchmarking Post-Hartree-Fock Methods To Describe the Nonlinear Optical Properties of Polymethines: An Investigation of the Accuracy of Algebraic Diagrammatic Construction (ADC) Approaches.

Third-order nonlinear optical (NLO) properties of polymethine dyes have been widely studied for applications such as all-optical switching. However, the limited accuracy of the current computational methodologies has prevented a comprehensive understanding of the nature of the lowest excited states and their influence on the molecular optical and NLO properties. Here, attention is paid to the lowest excited-state energies and their energetic ratio, as these characteristics impact the figure-of-merit for all-optical switching. For a series of model polymethines, we compare several algebraic diagrammatic construction (ADC) schemes for the polarization propagator with approximate second-order coupled cluster (CC2) theory, the widely used INDO/MRDCI approach and the symmetry-adapted cluster configuration interaction (SAC-CI) algorithm incorporating singles and doubles linked excitation operators (SAC-CI SD-R). We focus in particular on the ground-to-excited state transition dipole moments and the corresponding state dipole moments, since these quantities are found to be of utmost importance for an effective description of the third-order polarizability γ and two-photon absorption spectra. A sum-overstates expression has been used, which is found to quickly converge. While ADC(3/2) has been found to be the most appropriate method to calculate these properties, CC2 performs poorly.

Quantum Mechanical Identification of Quadrupolar Plasmonic Excited States in Silver Nanorods.

Quadrupolar plasmonic modes in noble metal nanoparticles have gained interest in recent years for various sensing applications. Although quantum mechanical studies have shown that dipolar plasmons can be modeled in terms of excited states where several to many excitations contribute coherently to the transition dipole moment, new approaches are needed to identify the quadrupolar plasmonic states. We show that quadrupolar states in Ag nanorods can be identified using the semiempirical INDO/SCI approach by examining the quadrupole moment of the transition density. The main longitudinal quadrupolar states occur at higher energies than the longitudinal dipolar states, in agreement with previous classical electrodynamics results, and have collective plasmonic character when the nanorods are sufficiently long. The ability to identify these states will make it possible to evaluate the differences between dipolar and quadrupolar plasmons that are relevant for sensing applications.

Semiempirical Modeling of Ag Nanoclusters: New Parameters for Optical Property Studies Enable Determination of Double Excitation Contributions to Plasmonic Excitation.

Quantum mechanical studies of Ag nanoclusters have shown that plasmonic behavior can be modeled in terms of excited states where collectivity among single excitations leads to strong absorption. However, new computational approaches are needed to provide understanding of plasmonic excitations beyond the single-excitation level. We show that semiempirical INDO/CI approaches with appropriately selected parameters reproduce the TD-DFT optical spectra of various closed-shell Ag clusters. The plasmon-like states with strong optical absorption comprise linear combinations of many singly excited configurations that contribute additively to the transition dipole moment, whereas all other excited states show significant cancellation among the contributions to the transition dipole moment. The computational efficiency of this approach allows us to investigate the role of double excitations at the INDO/SDCI level. The Ag cluster ground states are stabilized by slight mixing with doubly excited configurations, but the plasmonic states generally retain largely singly excited character. The consideration of double excitations in all cases improves the agreement of the INDO/CI absorption spectra with TD-DFT, suggesting that the SDCI calculation effectively captures some of the ground-state correlation implicit in DFT. These results provide the first evidence to support the commonly used assumption that single excitations are in many cases sufficient to describe the optical spectra of plasmonic excitations quantum mechanically.

Recognition of halides and Y-shaped oxoanions by carbonylchromium-based urea-like molecules: A theoretical analysis of hydrogen bonding modes.

One of the major challenges in anion recognition is to design hosts that can be used to distinguish between anions of different shapes. Urea-based molecules are widely used in anion recognition because the pair of -NH groups acts as an electron acceptor. Although these hosts can bind to both spherical anions (halides) and Y-shaped anions (oxoanions), experimental evidence to date does not provide a clear picture of what differences in the nature of the hydrogen bonding interactions could be used to distinguish between anions of different shapes. Here, we use several computational topology analyses to study the non-covalent interactions between Cr(CO)3-based organometallic urea-like hosts and halides and Y-shaped oxoanions. Our results suggest that the F(-) and AcO(-) anions are recognized experimentally due to a combination of strong interaction and large infrared (IR) shifts upon complexation, verifying the remarkable IR-reporting ability of the Cr(CO)3 moiety and its potential applications in anion recognition. The lone pairs of the oxygen atom in Y-shaped oxoanions directly interact with the -NH groups of the hosts, while all the shell electrons of the halides participate as a group in the interaction; however, the relative contributions of electrostatic and charge-transfer interactions are quite similar for the two types of anions. This insight into the nature of the anion-host interactions can be used to provide guidance for the design of hosts that differentiate between anions.

Distinguishing the Effects of Bond-Length Alternation versus Bond-Order Alternation on the Nonlinear Optical Properties of π-Conjugated Chromophores.

Understanding the relationships between the molecular nonlinear optical (NLO) properties and the bond-length alternation (BLA) or π-bond-order alternation (BOA) along the molecular backbone of linear π-conjugated systems has proven widely useful in the development of NLO organic chromophores and materials. Here, we examine model polymethines to elucidate the reliability of these relationships. While BLA is solely a measure of molecular geometric structure, BOA includes information pertaining to the electronic structure. As a result, BLA is found to be a good predictor of NLO properties only when optimized geometries are considered, whereas BOA is more broadly applicable. Proper understanding of the distinction between BLA and BOA is critical when designing computational studies of NLO properties, especially for molecules in complex environments or in nonequilibrium geometries.