Huzinaga projection embedding for efficient and accurate energies of systems with localized spin-densities.

We demonstrate the accuracy and efficiency of the restricted open-shell and unrestricted formulation of the absolutely localized Huzinaga projection operator embedding method. Restricted open-shell and unrestricted Huzinaga projection embedding in the full system basis is formally exact to restricted open-shell and unrestricted Kohn-Sham density functional theory, respectively. By utilizing the absolutely localized basis, we significantly improve the efficiency of the method while maintaining high accuracy. Furthermore, the absolutely localized basis allows for high accuracy open-shell wave function methods to be embedded into a closed-shell density functional theory environment. The open-shell embedding method is shown to calculate electronic energies of a variety of systems to within 1 kcal/mol accuracy of the full system wave function result. For certain highly localized reactions, such as spin transition energies on transition metals, we find that very few atoms are necessary to include in the wave function region in order to achieve the desired accuracy. This extension further broadens the applicability of our absolutely localized Huzinaga level-shift projection operator method to include open-shell species. Here, we apply our method to several representative examples, such as spin splitting energies, catalysis on transition metals, and radical reactions.

Plasmon-Mediated Intramolecular Methyl Migration with Nanoscale Spatial Control.

Plasmonic materials interact strongly with light to focus and enhance electromagnetic radiation down to nanoscale volumes. Due to this localized confinement, materials that support localized surface plasmon resonances are capable of driving energetically unfavorable chemical reactions. In certain cases, the plasmonic nanostructures are able to preferentially catalyze the formation of specific photoproducts, which offers an opportunity for the development of solar-driven chemical synthesis. Here, using plasmonic environments, we report inducing an intramolecular methyl migration reaction, forming 4-methylpyridine from N-methylpyridinium. Using both experimental and computational methods, we were able to confirm the identity of the N-methylpyridinium by making spectral comparisons against possible photoproducts. This reaction involves breaking a C-N bond and forming a new C-C bond, highlighting the ability of plasmonic materials to drive complex and selective reactions. Additionally, we observe that the product yield depends strongly on optical illumination conditions. This is likely due to steric hindrance in specific regions on the nanostructured plasmonic substrate, providing an optical handle for driving plasmonic catalysis with spatial specificity. This work adds yet another class of reactions accessible by surface plasmon excitation to the ever-growing library of plasmon-mediated chemical reactions.

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems.

Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal-ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal-organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. This work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

Absolutely Localized Projection-Based Embedding for Excited States.

We present a quantum embedding method that allows for calculation of local excited states embedded in a Kohn-Sham density functional theory (DFT) environment. Projection-based quantum embedding methodologies provide a rigorous framework for performing DFT-in-DFT and wave function in DFT (WF-in-DFT) calculations. The use of absolute localization, where the density of each subsystem is expanded in only the basis functions associated with the atoms of that subsystem, provide improved computationally efficiency for WF-in-DFT calculations by reducing the number of orbitals in the WF calculation. In this work, we extend absolutely localized projection-based quantum embedding to study localized excited states using EOM-CCSD-in-DFT and TDDFT-in-DFT. The embedding results are highly accurate compared to the corresponding canonical EOM-CCSD and TDDFT results on the full system, with TDDFT-in-DFT frequently more accurate than canonical TDDFT. The absolute localization method is shown to eliminate the spurious low-lying excitation energies for charge-transfer states and prevent overdelocalization of excited states. Additionally, we attempt to recover the environment response caused by the electronic excitations in the high-level subsystem using different schemes and compare their accuracy. Finally, we apply this method to the calculation of the excited-state energy of green fluorescent protein and show that we systematically converge to the full system results. Here we demonstrate how this method can be useful in understanding excited states, specifically which chemical moieties polarize to the excitation. This work shows absolutely localized projection-based quantum embedding can treat local electronic excitations accurately and make computationally expensive WF methods applicable to systems beyond current computational limits.

Projection-Based Correlated Wave Function in Density Functional Theory Embedding for Periodic Systems.

We present a level shift projection operator-based embedding method for systems with periodic boundary conditions-where the "active" subsystem can be described using either density functional theory (DFT) or correlated wave function (WF) methods and the "environment" is described using DFT. Our method allows for k-point sampling, is shown to be exactly equal to the canonical DFT solution of the full system under the limit that we use the full system basis to describe each subsystem, and can treat the active subsystem either with periodic boundary conditions-in what we term "periodic-in-periodic" embedding-or as a molecular cluster-in "cluster-in-periodic" embedding. We explore each of these methods and show that cluster WF-in-periodic DFT embedding can accurately calculate the absorption energy of CO on to a Si(100)-2×1 surface.

Single-Molecule Imaging Using Atomistic Near-Field Tip-Enhanced Raman Spectroscopy.

Advances in tip-enhanced Raman spectroscopy (TERS) have demonstrated ultrahigh spatial resolution so that the vibrational modes of individual molecules can be visualized. The spatial resolution of TERS is determined by the confinement of the plasmon-induced field in the junction; however, the conditions necessary for achieving the high spatial confinement required for imaging individual molecules are not fully understood. Here, we present a systematic theoretical study of TERS imaging of single molecules, using a hybrid atomistic electrodynamics-quantum mechanical method. This approach provides a consistent treatment of the molecule and the plasmonic near field under conditions where they cannot be treated separately. In our simulations, we demonstrate that TERS is capable of resolving intricate molecule vibrations with atomic resolution, although we find that TERS images are extremely sensitive to the near field in the junction. Achieving the atomic resolution requires the near field to be confined within a few ångstroms in diameter and the near-field focal plane to be in the molecule plane. Furthermore, we demonstrate that the traditional surface selection rule of Raman spectroscopy is altered due to the significant field confinement that leads to significant field-gradient effects in the Raman scattering. This work provides insights into single-molecule imaging based on TERS and Raman scattering of molecules in nanojunctions with atomic dimensions.

Improved Accuracy and Efficiency in Quantum Embedding through Absolute Localization.

Projection-based quantum embedding methodologies provide a framework for performing wave function-in-density functional theory (WF-in-DFT) calculations. The total WF-in-DFT energy is dependent on the partitioning of the total system and requires similar partitioning in each system for accurate energy differences. To achieve this, we enforce an absolute localization of the WF orbitals to basis functions only associated with the WF subsystem. This absolute localization, followed by iterative optimization of the subsystems' orbitals, provides improved energy differences for WF-in-DFT while simultaneously improving the computational efficiency.

Tip-Enhanced Raman Voltammetry: Coverage Dependence and Quantitative Modeling.

Electrochemical atomic force microscopy tip-enhanced Raman spectroscopy (EC-AFM-TERS) was employed for the first time to observe nanoscale spatial variations in the formal potential, E0', of a surface-bound redox couple. TERS cyclic voltammograms (TERS CVs) of single Nile Blue (NB) molecules were acquired at different locations spaced 5-10 nm apart on an indium tin oxide (ITO) electrode. Analysis of TERS CVs at different coverages was used to verify the observation of single-molecule electrochemistry. The resulting TERS CVs were fit to the Laviron model for surface-bound electroactive species to quantitatively extract the formal potential E0' at each spatial location. Histograms of single-molecule E0' at each coverage indicate that the electrochemical behavior of the cationic oxidized species is less sensitive to local environment than the neutral reduced species. This information is not accessible using purely electrochemical methods or ensemble spectroelectrochemical measurements. We anticipate that quantitative modeling and measurement of site-specific electrochemistry with EC-AFM-TERS will have a profound impact on our understanding of the role of nanoscale electrode heterogeneity in applications such as electrocatalysis, biological electron transfer, and energy production and storage.

Conformational Contrast of Surface-Mediated Molecular Switches Yields Ångstrom-Scale Spatial Resolution in Ultrahigh Vacuum Tip-Enhanced Raman Spectroscopy.

Tip-enhanced Raman spectroscopy (TERS) combines the ability of scanning probe microscopy (SPM) to resolve atomic-scale surface features with the single-molecule chemical sensitivity of surface-enhanced Raman spectroscopy (SERS). Here, we report additional insights into the nature of the conformational dynamics of a free-base porphyrin at room temperature adsorbed on a metal surface. We have interrogated the conformational switch between two metastable surface-mediated isomers of meso-tetrakis(3,5-ditertiarybutylphenyl)-porphyrin (H2TBPP) on a Cu(111) surface. At room temperature, the barrier between the porphyrin ring buckled up/down conformations of the H2TBPP-Cu(111) system is easily overcome, and a 2.6 Å lateral resolution by simultaneous TERS and STM analysis is achieved under ultrahigh vacuum (UHV) conditions. This work demonstrates the first UHV-TERS on Cu(111) and shows TERS can unambiguously distinguish the conformational differences between neighboring molecules with Ångstrom-scale spatial resolution, thereby establishing it as a leading method for the study of metal-adsorbate interactions.

Simulating Surface-Enhanced Hyper-Raman Scattering Using Atomistic Electrodynamics-Quantum Mechanical Models.

Surface-enhanced hyper-Raman scattering (SEHRS) is the two-photon analogue of surface-enhanced Raman scattering (SERS), which has proven to be a powerful tool to study molecular structures and surface enhancements. However, few theoretical approaches to SEHRS exist and most neglect the atomistic descriptions of the metal surface and molecular resonance effects. In this work, we present two atomistic electrodynamics-quantum mechanical models to simulate SEHRS. The first is the discrete interaction model/quantum mechanical (DIM/QM) model, which combines an atomistic electrodynamics model of the nanoparticle with a time-dependent density functional theory description of the molecule. The second model is a dressed-tensors method that describes the molecule as a point-dipole and point-quadrupole object interacting with the enhanced local field and field-gradients (FG) from the nanoparticle. In both of these models, the resonance effects are treated efficiently by means of damped quadratic response theory. Using these methods, we simulate SEHRS spectra for benzene and pyridine. Our results show that the FG effects in SEHRS play an important role in determining both the surface selection rules and the enhancements. We find that FG effects are more important in SEHRS than in SERS. We also show that the spectral features of small molecules can be accurately described by accounting for the interactions between the molecule and the local field and FG of the nanoparticle. However, at short distances between the metal and molecule, we find significant differences in the SEHRS enhancements predicted using the DIM/QM and the dressed-tensors methods.

Theory of Linear and Nonlinear Surface-Enhanced Vibrational Spectroscopies.

The vibrational spectroscopy of molecules adsorbed on metal nanoparticles can be enhanced by many orders of magnitude so that the detection and identification of single molecules are possible. The enhancement of most linear and nonlinear vibrational spectroscopies has been demonstrated. In this review, we discuss theoretical approaches to understanding linear and nonlinear surface-enhanced vibrational spectroscopies. A unified description of enhancement mechanisms classified as either electromagnetic or chemical in nature is presented. Emphasis is placed on understanding the spectral changes necessary for interpretation of linear and nonlinear surface-enhanced vibrational spectroscopies.

External orthogonality in subsystem time-dependent density functional theory.

Subsystem density functional theory (subsystem DFT) is a DFT partitioning method that is exact in principle, but depends on approximations to the kinetic energy density functional (KEDF). One may avoid the use of approximate KEDFs by ensuring that the inter-subsystem molecular orbitals are orthogonal, termed external orthogonality (EO). We present a method that extends a subsystem DFT method, that includes EO, into the time-dependent DFT (TDDFT) regime. This method therefore removes the need for approximations to the kinetic energy potential and kernel, and we show that it can accurately reproduce the supermolecular TDDFT results for weakly and strongly coupled subsystems, and for systems with strongly overlapping densities (where KEDF approximations traditionally fail).

Frozen Density Embedding with External Orthogonality in Delocalized Covalent Systems.

Frozen density embedding (FDE) has become a popular subsystem density functional theory (DFT) method for systems with weakly overlapping charge densities. The failure of this method for strongly interacting and covalent systems is due to the approximate kinetic energy density functional (KEDF), although the need for approximate KEDFs may be eliminated if each subsystem's Kohn-Sham (KS) orbitals are orthogonal to the other, termed external orthogonality (EO). We present an implementation of EO into the FDE framework within the Amsterdam density functional program package, using the level-shift projection operator method. We generalize this method to remove the need for orbital localization schemes and to include multiple subsystems, and we show that the exact KS-DFT energies and densities may be reproduced through iterative freeze-and-thaw cycles for a number of systems, including a charge delocalized benzene molecule starting from atomic subsystems. Finally, we examine the possibility of a truncated basis for systems with and without charge delocalization, and found that subsystems require a basis that allows them to correctly describe the supermolecular delocalized orbitals.

Molecular-Resolution Interrogation of a Porphyrin Monolayer by Ultrahigh Vacuum Tip-Enhanced Raman and Fluorescence Spectroscopy.

Tip-enhanced Raman scattering (TERS) and optically excited tip-enhanced fluorescence (TEF) of a self-assembled porphyrin monolayer on Ag(111) are studied using an ultrahigh vacuum scanning tunneling microscope (UHV-STM). Through selectively exciting different Q-bands of meso-tetrakis- (3,5-ditertiarybutylphenyl)-porphyrin (H2TBPP), chemical information regarding different vibronic excited states is revealed by a combination of theory and experiment; namely, TERS and time-dependent density functional theory (TDDFT) simulations. The observed TEF spectra suggest a weak coupling of H2TBPP to the substrate due to the bulky t-butyl groups and a possible alternative excited state decay path. This work demonstrates the potential of combining TERS and TEF for studying surface-mounted porphyins on substrates, thus providing insight into porphyrin-sensitized solar cells and catalysis.

Plasmonic circular dichroism of 310- and α-helix using a discrete interaction model/quantum mechanics method.

Plasmonic circular dichroism (CD) of chiral molecules in the near field of plasmonic nanoparticles (NPs) may be used to enhance molecular CD signatures or to induce a CD signal at the plasmon resonance. A recent few-states theory explored these effects for model systems and showed an orientation dependence of the sign of the induced CD signal for spherical NPs. Here, we use the discrete interaction model/quantum mechanical (DIM/QM) method to simulate the CD and plasmonic CD of the 310- and α-helix conformations of a short alanine peptide. We find that the interactions between the molecule and the plasmon lead to significant changes in the CD spectra. In the plasmon region, we find that the sign of the CD depends strongly on the orientation of the molecule as well as specific interactions with the NP through image dipole effects. A small enhancement of the CD is found in the molecular region of the spectrum, however, the molecular signatures may be significantly altered through interactions with the NP. We also show that the image dipole effect can result in induced plasmonic CD even for achiral molecules. Overall, we find that the specific interactions with the NP can lead to large changes to the CD spectrum that complicates the interpretation of the results.

Simulating surface-enhanced Raman optical activity using atomistic electrodynamics-quantum mechanical models.

Raman optical activity has proven to be a powerful tool for probing the geometry of small organic and biomolecules. It has therefore been expected that the same mechanisms responsible for surface-enhanced Raman scattering may allow for similar enhancements in surface-enhanced Raman optical activity (SEROA). However, SEROA has proved to be an experimental challenge and mirror-image SEROA spectra of enantiomers have so far not been measured. There exists a handful of theories to simulate SEROA, all of which treat the perturbed molecule as a point-dipole object. To go beyond these approximations, we present two new methods to simulate SEROA: the first is a dressed-tensors model that treats the molecule as a point-dipole and point-quadrupole object; the second method is the discrete interaction model/quantum mechanical (DIM/QM) model, which considers the entire charge density of the molecule. We show that although the first method is acceptable for small molecules, it fails for a medium-sized one such as 2-bromohexahelicene. We also show that the SEROA mode intensities and signs are highly sensitive to the nature of the local electric field and gradient, the orientation of the molecule, and the surface plasmon frequency width. Our findings give some insight into why experimental SEROA, and in particular observing mirror-image SEROA for enantiomers, has been difficult.