Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Higher-order diagrammatic vibrational coupled-cluster theory.

Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies of a molecule, the latter through the equation-of-motion (EOM) formalism, is defined for an nth-order Taylor-series potential energy surface (PES). Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman-Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC including up to the mth-order excitation operators are derived and implemented with the aid of computer algebra in the range of 1 ≤ m ≤ 8. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation, reducing the cost scaling of the mth-order XVCC and EOM-XVCC in an nth-order Taylor-series PES (m ≥ n) to the optimal value of O(N(m+⌊n/2⌋)), where N is the number of modes. The calculated zero-point energies and frequencies of fundamentals, overtones, and combinations as well as Fermi-resonant modes display rapid and nearly monotonic convergence with m towards the exact values for the PES. The theory with the same excitation rank as the truncation order of the Taylor-series PES (m = n) seems to strike the best cost-accuracy balance, achieving the accuracy of a few tenths of cm(-1) for transitions involving (m - 3) modes and of a few cm(-1) for those involving (m - 2) modes. The relationships between XVCC and the vibrational coupled-cluster theories of Prasad and coworkers and of Christiansen and coworkers as well as the size-extensive vibrational self-consistent-field and many-body perturbation theories are also elucidated.

Plasmon Resonances of Semiconductor Nanocrystals: Physical Principles and New Opportunities.

The discovery of localized surface plasmon resonances (LSPRs) in doped semiconductor nanocrystals has opened a new regime in plasmonics. We address both the technological and fundamental advances made possible by the realization of LSPRs in semiconductor nanocrystals. LSPRs were originally thought to be specific only to metallic nanostructures, but since their manifestation in semiconductor nanostructures, LSPRs are being seen as ubiquitous optical signatures of charge carriers. As fingerprints of a charge carrier collection, LSPRs of semiconductors are emerging as optical probes of processes that involve carrier dynamics, including redox reactions, electrochemistry, phase transitions, and photocatalysis. Unlike their electrical counterparts, LSPRs allow remote contactless probing and minimal device design. Ultrasmall semiconductor quantum dots are now enabling access to plasmon resonances of a handful of charge carriers, allowing us to ask fundamental questions regarding the lower limit of charge carriers needed to sustain a plasmon resonance, the emergence of a collective mode from a single-electron transition, and the effect of quantum confinement on plasmon resonances. These fundamental issues are discussed here, along with the need for new physical models required to capture the unique aspects of semiconductor LSPRs.

Doped nanocrystals as plasmonic probes of redox chemistry.

A (nano)crystal-clear view: With doped semiconductor nanocrystals, local chemical events can be probed through their perturbation of the carrier density of the nanocrystal. Examples demonstrate that redox processes and ligand chemistry can induce changes in the vacancy density within copper(I) sulfide nanorods, allowing such events to be detected by strong shifts in localized surface plasmon resonance.