The position operator problem in periodic calculations with an emphasis on theoretical spectroscopy.

In this article, we present the challenges that arise when carrying out spectroscopic simulations within periodic boundary conditions. We present approaches which were proposed in the literature for the calculation of the extension of the electric dipole moment to periodic systems. Further, we describe the challenges arising for the simulation of magnetic properties within periodic boundary conditions and for the simulation of nuclear magnetic resonance shielding tensors and related quantities. Furthermore, issues arising in periodic implementations of vibrational circular dichroism spectroscopy are described, especially for the case of atom-centered basis functions and nuclear velocity perturbation theory.

BODIPY-Based Photothermal Agents with Excellent Phototoxic Indices for Cancer Treatment.

Here, we report six novel, easily accessible BODIPY-based agents for cancer treatment. In contrast to established photodynamic therapy (PDT) agents, these BODIPY-based compounds show additional photothermal activity and their cytotoxicity is not dependent on the generation of reactive oxygen species (ROS). The agents show high photocytotoxicity upon irradiation with light and low dark toxicity in different cancer cell lines in 2D culture as well as in 3D multicellular tumor spheroids (MCTSs). The ratio of dark to light toxicity (phototoxic index, PI) of these agents reaches striking values exceeding 830,000 after irradiation with energetically low doses of light at 630 nm. The oxygen-dependent mechanism of action (MOA) of established photosensitizers (PSs) hampers effective clinical deployment of these agents. Under hypoxic conditions (0.2% O2), which are known to limit the efficiency of conventional PSs in solid tumors, photocytotoxicity was induced at the same concentration levels, indicating an oxygen-independent photothermal MOA. With a PI exceeding 360,000 under hypoxic conditions, both PI values are the highest reported to date. We anticipate that small molecule agents with a photothermal MOA, such as the BODIPY-based compounds reported in this work, may overcome this barrier and provide a new avenue to cancer therapy.

Automatic purpose-driven basis set truncation for time-dependent Hartree-Fock and density-functional theory.

Real-time time-dependent density-functional theory (RT-TDDFT) and linear response time-dependent density-functional theory (LR-TDDFT) are two important approaches to simulate electronic spectra. However, the basis sets used in such calculations are usually the ones designed mainly for electronic ground state calculations. In this work, we propose a systematic and robust scheme to truncate the atomic orbital (AO) basis set employed in TDDFT and TD Hartree-Fock (TDHF) calculations. The truncated bases are tested for both LR- and RT-TDDFT as well as RT-TDHF approaches, and provide an acceleration up to an order of magnitude while the shifts of excitation energies of interest are generally within 0.2 eV. The procedure only requires one extra RT calculation with 1% of the total propagation time and a simple modification on basis set file, which allows an instant application in any quantum chemistry package supporting RT-/LR-TDDFT calculations. Aside from the reduced computational effort, this approach also offers valuable insight into the effect of different basis functions on computed electronic excitations and further ideas on the design of basis sets for special purposes.

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.

Time Domain Simulation of (Resonance) Raman Spectra of Liquids in the Short Time Approximation.

Real-time time-dependent density functional theory (RT-TDDFT) and ab initio molecular dynamics (AIMD) are combined to calculate non-resonant and resonant Raman scattering cross sections of periodic systems, allowing for an explicit quantum mechanical description of condensed phase systems and environmental effects. It is shown that this approach to Raman spectroscopy corresponds to a short time approximation of Heller's time-dependent formalism for the description of Raman scattering. Two ways to calculate the frequency-dependent polarizability in a periodic system are presented: (1) via the modern theory of polarization (Berry phase) and (2) via the velocity representation. Both approaches are found to be equivalent for a system of liquid (S)-methyloxirane with the computational settings used. Resulting non-resonance and resonance Raman spectra from the dynamic AIMD/RT-TDDFT approach are compared to the spectra of one gas phase molecule in the harmonic approximation highlighting finite temperature and solvation effects. Using RT-TDDFT to calculate the full frequency-dependent Placzek-type polarizability within one set of simulations covers the non-resonance, near-resonance, and on-resonance regimes on equal footing, thus allowing the calculation of full Raman excitation profiles.

Vibrational (resonance) Raman optical activity with real time time dependent density functional theory.

We present a novel approach for the calculation of vibrational (resonance) Raman optical activity (ROA) spectra based on real time propagation. The ROA linear electronic response tensors are formulated in a propagator formalism in order to treat linear response (LR-) and real time time dependent density functional theory (RT-TDDFT) on equal footing. The length, mixed, and velocity representations of these tensors are discussed with respect to the potential origin dependence of the ROA invariants in the calculations. The propagator formalism allows a straight forward extension of the optical LR tensors in a mixed or velocity representation to a coupling with nonlocal potentials, where an extra term appears in the definition of the momentum operator, in order to maintain the gauge invariance. Using RT-TDDFT paves the way for an innovative, efficient calculation of both on- and off-resonance ROA spectra. Exemplary results are given for the off-resonance and (pre-)resonance spectra of (R)-methyloxirane, considering the resonance effects due to one or more electronically excited states. Moreover, the developed real time propagation approach allows us to obtain entire excitation profiles in a computationally efficient way.

Efficient calculation of (resonance) Raman spectra and excitation profiles with real-time propagation.

We investigate approaches for the calculation of (resonance) Raman spectra in a real-time time-dependent density functional theory (RT-TDDFT) framework. Several short time approximations to the Kramers, Heisenberg, and Dirac polarizability tensor are examined with regard to the calculation of resonance Raman spectra: One relies on a Placzek type expansion of the electronic polarizability and the other one relies on the excited state gradient method. The first one is shown to be in agreement with an approach based on perturbation theory in the case of a weak δ-pulse perturbation. The latter is newly applied in a real time propagation framework, enabled by the use of Padé approximants to the Fourier transform which allow for a sufficient resolution in the frequency domain. An analysis of the performance of Padé approximants is given. All approaches were found to be in good agreement for uracil and R-methyloxirane. Moreover it is shown how RT-TDDFT can be used to calculate Raman excitation profiles efficiently.

Effects of tunnelling and asymmetry for system-bath models of electron transfer.

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.