Tip-enhanced Raman spectroscopy (TERS) provides chemical information for adsorbates with nanoscale spatial resolution, single-molecule sensitivity, and, when combined with scanning tunneling microscopy (STM), Ångstrom-scale topographic resolution. Performing TERS under ultrahigh-vacuum conditions allows pristine and atomically smooth surfaces to be maintained, while liquid He cooling minimizes surface diffusion of adsorbates across the solid surface, allowing direct STM imaging. Low-temperature TER (LT-TER) spectra differ from room-temperature TER (RT-TER), RT surface-enhanced Raman (SER), and LT-SER spectra because the vibrational lines are narrowed and shifted, revealing additional chemical information about adsorbate-substrate interactions. As an example, we present LT-TER spectra for the rhodamine 6G (R6G)/Ag(111) system that exhibit such unique spectral shifts. The high spectral resolution of LT-TERS provides intramolecular insight in that the shifted modes are associated with the ethylamine moiety of R6G. LT-TERS is a promising approach for unraveling the intricacies of adsorbate-substrate interactions that are inaccessible by other means.

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.

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.

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.

We present a quantum embedding method that allows for the 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 1 arXiv:1909.12423v1 [physics.chem-ph] 26 Sep 2019 absolute localization method is shown to eliminate the spurious low-lying excitation energies for charge transfer states and prevent over delocalization 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. many systems. 16 However, the computational cost of EOM-CCSD (scaling as O(N 6 )) restricts its usage to about 50 or fewer atoms in a moderate basis. Methods that extend the applicability of EOM-CCSD to larger systems include the use of local orbitals, [17][18][19][20][21] restricted virtual spaces, 22,23 and multiscale approaches. [24][25][26][27] Multiscale approaches treat different regions of the molecule with methods of varying cost and accuracy to reflect their importance. 28,29 For example, one may use EOM-CCSD to describe the important region of the molecule while using molecular mechanics (MM), in EOM-CCSD-in-MM methods, [30][31][32] or DFT, in EOM-CCSD-in-DFT methods, 33 to describe the remainder of the molecule. Such approaches take advantage of the high accuracy of EOM-CCSD and the low scaling of MM or DFT to go beyond the size/accuracy limits of any one method alone.Density functional theory embedding provides a formally exact framework for performing multiscale calculations. This approach has been shown to be accurate for combining density functional theory with wave function theory. The key choice in density function theory embedd...