Real-time time-dependent density functional theory implementation of electronic circular dichroism applied to nanoscale metal-organic clusters

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Time Evolution of Plasmonic Features in Pentagonal Ag Clusters

In the present work, we apply recently developed real-time descriptors to study the time evolution of plasmonic features of pentagonal Ag clusters. The method is based on the propagation of the time-dependent Schrödinger equation within a singly excited TDDFT ansatz. We use transition contribution maps (TCMs) and induced density to characterize the optical longitudinal and transverse response of such clusters, when interacting with pulses resonant with the low-energy (around 2-3 eV, A1) size-dependent or the high-energy (around 4 eV, E1) size-independent peak. TCMs plots on the analyzed clusters, Ag25+ and Ag43+ show off-diagonal peaks consistent with a plasmonic response when a longitudinal pulse resonant at A1 frequency is applied, and dominant diagonal spots, typical of a molecular transition, when a transverse E1 pulse is employed. Induced densities confirm this behavior, with a dipole-like charge distribution in the first case. The optical features show a time delay with respect to the evolution of the external pulse, consistent with those found in the literature for real-time TDDFT calculations on metal clusters.

Electronic circular dichroism from real-time propagation in state space

In this paper, we propose to compute the electronic circular dichroism (ECD) spectra of chiral molecules using a real-time propagation of the time-dependent Schrödinger equation (TDSE) in the space of electronic field-free eigenstates, by coupling TDSE with a given treatment of the electronic structure of the target. The time-dependent induced magnetic moment is used to compute the ECD spectrum from an explicit electric perturbation. The full matrix representing the transition magnetic moment in the space of electronic states is generated from that among pairs of molecular orbitals. In the present work, we show the ECD spectra of methyloxirane, of several conformers of L-alanine, and of the Λ-Co(acac)₃ complex, computed from a singly excited ansatz of time-dependent density functional theory eigenstates. The time-domain ECD spectra properly reproduce the frequency-domain ones obtained in the linear-response regime and quantitatively agree with the available experimental data. Moreover, the time-domain approach to ECD allows us to naturally go beyond the ground-state rotationally averaged ECD spectrum, which is the standard outcome of the linear-response theory, e.g., by computing the ECD spectra from electronic excited states.

Comparison of Length, Velocity, and Symmetric Gauges for the Calculation of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory

A velocity and symmetric gauge implementation for real-time time-dependent density functional theory (RT-TDDFT) in the CP2K package using a Gaussian and plane wave approach is presented, including the explicit gauge-transformed contributions due to the nonlocal part of pseudopotentials. Absorption spectra of gas-phase α-pinene are calculated in length and velocity gauges in the long-wavelength approximation for the application of a δ pulse in linear and full order. The velocity gauge implementation is also applied to a solvated uracil molecule to showcase its use within periodic boundary conditions (PBC). For the calculation of the expectation value of the electric dipole moment in PBC, both the velocity representation and the modern theory of polarization give equivalent absorption spectra if a distributed reference point is used for the nonlocal term of the velocity operator. The discussion of linear response theory takes place in a unified framework in terms of linear response functions in propagator notation, distinguishing the parts of the linear response functions associated with perturbation and response. To further investigate gauge dependence, electric circular dichroism (ECD) spectra of α-pinene were calculated either as magnetic response to an electric field perturbation, in length or velocity gauge, or as electric response to a magnetic field perturbation in the symmetric gauge. Both approaches, electric and magnetic perturbations, have been found to yield equivalent ECD spectra.

Impact of Adsorption of Straight Chain Alcohol Molecules on the Optical Properties of Calcite (10.4) Surface

Calcium carbonate plays a central role in controlling the chemistry of the oceans, biomineralization and oil production, to name a few. In this work, using density functional theory with semiempirical dispersion corrections and simplified TD-DFT using Tamm-Dancoff approximation, we investigated the impact of the adsorption of straight chain alcohol (ethanol and pentanol) molecules on the optical properties of a calcite (10.4) surface. Our results show that ethanol and/or pentanol molecules form a well-ordered monolayer (through their hydroxyl group with carbon chains sticking away in a standing-up position) on the calcite (10.4) surface. Additionally, we found intriguing modulations in the photoabsorption spectra and circular dichroism spectra. In particular, the latter was a unique optical fingerprint for a molecule-adsorbed calcite (10.4) surface. Our findings provide useful insights into the structural and optical features of calcite-based systems at the atomic level.

Influence of Au, Ag, and Cu Adatoms on Optical Properties of TiO2 (110) Surface: Predictions from RT-TDDFT Calculations

In this paper, real-time time-dependent density-functional theory (RT-TDDFT) calculations are performed to analyze the optical property and charge transitions of a single noble metal atom deposited on rutile TiO2 (110) surface. The model structures are built reflecting the equilibrium positions of deposited adatoms atop the TiO2 surface. The absorption spectra are calculated for all model structures under study. To provide deeper insight into photo-absorption processes, the transition contribution maps are computed for the states of deposited adatoms involved in transitions. Assuming the photon energy is enough to overcome the band gap of TiO2 (∼3 eV), the photogenerated electrons of TiO2 seem to be partly accumulated around deposited Au atoms. In contrast, this is rarely observed for deposited Ag and Cu atoms. Based on our calculations, we have identified the transition state mechanism that is important for the design strategy of future photocatalytic materials.

Absolute configuration retention of a configurationally labile ligand during dynamic processes of thiolate protected gold clusters

Monolayer protected metal clusters are dynamic nanoscale objects. For example, the chiral Au38(2-PET)24 cluster (2-PET: 2-phenylethylthiolate) racemizes at moderate temperature. In addition, ligands and metal atoms can easily exchange between clusters. Such processes are important for applications of monolayer protected metal clusters; however, the mechanistic study of such processes turns out to be challenging. Here we use a configurationally labile, axially chiral ligand, biphenyl-2,2'-dithiol (R/S-BiDi), as a probe to study dynamic cluster processes. It is shown that the ligand exchange of free R/S-BiDi on a chiral Au38(2-PET)24 cluster is diastereospecific. Using chiral chromatography, isolated single diastereomers of the type anticlockwise/clockwise-Au38(2-PET)22(R/S-BiDi)1 could be isolated. Upon heating, the cluster framework racemizes, while the R/S-BiDi ligand does not. These findings demonstrate that during cluster racemization and/or ligand exchange between clusters, the R/S-BiDi ligand is sufficiently confined, thus preventing its racemization, and exclude the possibility that the ligand desorbs from the cluster surface.