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

Propagated (fragment) Pipek-Mezey Wannier functions in real-time time-dependent density functional theory

Localization procedures are an important tool for analysis of complex systems in quantum chemistry, since canonical molecular orbitals are delocalized and can, therefore, be difficult to align with chemical intuition and obscure information at the local level of the system. This especially applies to calculations obeying periodic boundary conditions. The most commonly used approach to localization is Foster-Boys Wannier functions, which use a unitary transformation to jointly minimize the second moment of the orbitals. This procedure has proven to be robust and fast but has a side effect of often mixing σ- and π-type orbitals. σ/π-separation is achieved by the Pipek-Mezey Wannier function (PMWF) approach [Lehtola and Jónsson, J. Chem. Theory Comput. 10, 642 (2014) and Jónsson et al., J. Chem. Theory Comput. 13, 460 (2017)], which defines the spread functional in terms of partial charges instead. We have implemented a PMWF algorithm in the CP2K software package using the Cardoso-Souloumiac algorithm to enable their application to real-time time-dependent density functional theory. The method is demonstrated on stacked CO2 molecules, linear acetylenic carbon, boron and nitrogen co-doped graphene, and nitrogen-vacancy doped diamond. Finally, we discuss its computational scaling and recent efforts to improve it with fragment approaches.

Chiral Spectroscopy of Bulk Systems with Propagated Localized Orbitals

We present approaches for the simulation of electronic circular dichroism, Raman, and Raman optical activity (ROA) spectra for isolated and periodic systems as well as subsystem analysis thereof. The method is based on the use of time-dependent maximally localized Wannier functions in the CP2K package and accounts for origin dependencies inherent to the Gaussian and plane wave with pseudopotentials approach as well as the origin dependence of the magnetic dipole and electric quadrupole operators. Tests on the H-bonded enantiomers of alanine by harmonic normal-mode analysis and on an aqueous solution of l-alanine by ab initio molecular dynamics obeying periodic boundary conditions (PBCs) are presented as total and subsystem-resolved spectra. To our knowledge, this is the first instance of an ROA spectrum derived from real-time propagation obeying PBCs and the first ROA simulation considering off-, pre-, and on-resonance effects within PBCs.

Computational Design of Molecular Probes for Electronic Preresonance Raman Scattering Microscopy

Recently developed electronic preresonance stimulated Raman scattering (epr-SRS) microscopy, in which the Raman signal of a dye is significantly boosted by setting the incident laser frequency near the electronic excitation energy, has pushed the sensitivity of SRS microscopy close to that offered by confocal fluorescence microscopy. Prominently, the maintained narrow line-width of epr-SRS also offers high multiplexity that breaks the "color barrier" in optical microscopy. However, detailed understanding of the fundamental mechanism in these epr-SRS dyes still remains elusive. Here, we combine experiments with theoretical modeling to investigate the structure-function relationship, aiming to facilitate the design of new probes and expanding epr-SRS palettes. Our ab initio approach employing the displaced harmonic oscillator (DHO) model provides a consistent agreement between simulated and experimental SRS intensities of various triple-bond bearing epr-SRS probes with distinct scaffolds. We further review two popular approximate expressions for epr-SRS, namely the short-time and Albrecht A-term equations, and compare them to the DHO model. Overall, the theory allows us to illustrate how the observed intensity differences between molecular scaffolds stem from the coupling strength between the electronic excitation and the targeted vibrational mode, leading to a general design strategy for highly sensitive next-generation vibrational imaging probes.

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.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

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.

A Concise Review on Recent Developments of Machine Learning for the Prediction of Vibrational Spectra

Machine learning has become more and more popular in computational chemistry, as well as in the important field of spectroscopy. In this concise review, we walk the reader through a short summary of machine learning algorithms and a comprehensive discussion on the connection between machine learning methods and vibrational spectroscopy, particularly for the case of infrared and Raman spectroscopy. We also briefly discuss state-of-the-art molecular representations which serve as meaningful inputs for machine learning to predict vibrational spectra. In addition, this review provides an overview of the transferability and best practices of machine learning in the prediction of vibrational spectra as well as possible future research directions.

Local approaches for electric dipole moments in periodic systems and their application to real-time time-dependent density functional theory

Within periodic boundary conditions, the traditional quantum mechanical position operator is ill-defined, necessitating the use of alternative methods, most commonly the Berry phase formulation in the modern theory of polarization. Since any information about local properties is lost in this change of framework, the Berry phase formulation can only determine the total electric polarization of a system. Previous approaches toward recovering local electric dipole moments have been based on applying the conventional dipole moment operator to the centers of maximally localized Wannier functions (MLWFs). Recently, another approach to local electric dipole moments has been demonstrated in the field of subsystem density functional theory (DFT) embedding. We demonstrate in this work that this approach, aside from its use in ground state DFT-based molecular dynamics, can also be applied to obtain electric dipole moments during real-time propagated time-dependent DFT (RT-TDDFT). Moreover, we present an analogous approach to obtain local electric dipole moments from MLWFs, which enables subsystem analysis in cases where DFT embedding is not applicable. The techniques were implemented in the quantum chemistry software CP2K for the mixed Gaussian and plane wave method and applied to cis-diimide and water in the gas phase, cis-diimide in aqueous solution, and a liquid mixture of dimethyl carbonate and ethylene carbonate to obtain absorption and infrared spectra decomposed into localized subsystem contributions.

Ab Initio Surface-Hopping Simulation of Femtosecond Transient-Absorption Pump-Probe Signals of Nonadiabatic Excited-State Dynamics Using the Doorway-Window Representation

An ab initio theoretical framework for the simulation of femtosecond time-resolved transient absorption (TA) pump-probe (PP) spectra with quasi-classical trajectories is presented. The simulations are based on the classical approximation to the doorway-window (DW) representation of third-order four-wave-mixing signals. The DW formula accounts for the finite duration and spectral shape of the pump and probe pulses. In the classical DW formalism, classical trajectories are stochastically sampled from a positive definite doorway distribution, and the signals are evaluated by averaging over a positive definite window distribution. Nonadiabatic excited-state dynamics is described by a stochastic surface-hopping algorithm. The method has been implemented for the pyrazine molecule with the second-order algebraic-diagrammatic construction (ADC(2)) ab initio electronic-structure method. The methodology is illustrated by ab initio simulations of the ground-state bleach, stimulated emission, and excited-state absorption contributions to the TA PP spectrum of gas-phase pyrazine.

Analytic calculation and analysis of atomic polar tensors for molecules and materials using the Gaussian and plane waves approach

The evaluation of atomic polar tensors and Born Effective Charge (BEC) tensors from Density Functional Perturbation Theory (DFPT) has been implemented in the CP2K code package. This implementation is based on a combination of the Gaussian and plane wave approach for the description of basis functions and arising potentials. The presence of non-local pseudo-potentials has been considered, as well as contributions arising from the basis functions being centered on the atoms. Simulations of both periodic and non-periodic systems have been implemented and carried out. Dipole strengths and infrared absorption spectra have been calculated for two isomers of the tripeptide Ser-Pro-Ala using DFPT and are compared to the results of standard vibrational analyses using finite differences. The spectra are then decomposed into five subsets by employing localized molecular orbitals/maximally localized Wannier functions, and the results are discussed. Moreover, group coupling matrices are employed for visualization of results. Furthermore, the BECs and partial charges of the surface atoms of a periodic (101) anatase (TiO₂) slab have been investigated in a periodic framework.