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

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.

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.

New chiral ECD-Raman spectroscopy of atropisomeric naphthalenediimides

In this study, we found that a recently discovered ECD-Raman effect dominated over the natural Raman optical activity in a series of atropisomeric naphthalenediimides, and we investigated the kind of information about the molecular structure that could be obtained from the spectra. The ECD-Raman effect is polarised Raman scattering modulated by electronic circular dichroism. We showed that the spectra significantly depended on the substitution of the solute and/or the change of the solvent. Moreover, the spectra could be well-predicted by the theory, thus providing an interesting tool to monitor the chirality of the binaphthyl compounds.

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.

Classical Trajectory of Molecules in Electromagnetic Field: A Handy Method to Simulate Molecular Vibrational Spectra

Within harmonic approximations, molecular vibrational spectra are simulated in a standard way through force field diagonalization and following transformation of Cartesian to normal-mode tensor derivatives. This may become tedious for large systems of many thousands of atoms and also not necessary because of a limited resolution required to interpret an experiment. We developed an algorithm based on the real-time real-field molecular dynamics, effectively at zero temperature, invoked in a molecule by the electromagnetic field of light. The algorithm is simple to implement and suitable for parallel computing, and it can be potentially extended to more complicated molecular-light interaction modes. It circumvents the diagonalization and is suitable to model vibrational optical activity (vibrational circular dichroism and, to a lesser extent, Raman optical activity). For large molecules, it becomes faster than diagonalization, but it also enables the assignment of vibrational spectral bands to local molecular motions.

Measurement and Theory of Resonance Raman Optical Activity for Gases, Liquids, and Aggregates. What It Tells about Molecules

Resonance Raman Optical Activity (RROA) appeared as a natural extension of the nonresonance branch. It combines the structural sensitivity of chiroptical spectroscopy with the signal enhancement coming from the resonance of molecular electronic transitions with the excitation laser light. However, the idea has been hampered by many technical and theoretical problems that are being clarified only in recent years. We provide the theoretical basis and several examples documenting the problems, achievements, and potential of RROA, in particular in biomolecular studies.

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.

Recognition of the True and False Resonance Raman Optical Activity

Resonance Raman optical activity (RROA) possesses all aspects of a sensitive tool for molecular detection, but its measurement remains challenging. We demonstrate that reliable recording of RROA of chiral colorful compounds is possible, but only after considering the effect of the electronic circular dichroism (ECD) on the ROA spectra induced by the dissolved chiral compound. We show RROA for a number of model vitamin B12 derivatives that are chemically similar but exhibit distinctively different spectroscopic behavior. The ECD/ROA effect is proportional to the concentration and dependent on the optical pathlength of the light propagating through the sample. It can severely alter relative band intensities and signs in the natural RROA spectra. The spectra analyses are supported by computational modeling based on density functional theory. Neglecting the ECD effect during ROA measurement can lead to misinterpretation of the recorded spectra and erroneous conclusions about the molecular structure.

Can One Measure Resonance Raman Optical Activity?

Resonance Raman optical activity (RROA) is commonly measured as the difference in intensity of Raman scattered right and left circularly polarized light, I_R -I_L , when a randomly polarized light is in resonance with a chiral molecule. Strong and sometimes mono-signate experimental RROA spectra of several chiral solutes were reported previously, although their signs and relative intensities could not be reproduced theoretically. By examining multiple light-matter interaction events which can occur simultaneously under resonance, we show that a new form of chiral Raman spectroscopy, eCP-Raman, a combination of electronic circular dichroism and circularly polarized Raman, prevails. By incorporating the finite-lifetime approach for resonance, the experimental patterns of the model chiral solutes are captured theoretically by eCP-Raman, without any RROA contribution. The results open opportunity for applications of eCP-Raman spectroscopy and for extracting true RROA experimentally.

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.

On Raman optical activity sign-switching between the ground and excited states leading to an unusual resonance ROA induced chirality

Raman optical activity (ROA) spectra recorded for a chiral naphthalene diimide derivative (nBu-NDI–BINAM) dissolved in a series of solvents exhibit strong solute to solvent induced chirality with: (1) dominating bands of solvents, (2) nBu-NDI–BINAM resonance ROA (RROA) bands which are barely visible, (3) monosignate RROA Solvent spectra with an unexpected sign concordant with that of the ECD band of the resonant electronic state, (4) bisignate RROA bands for a few solvents, and (5) superposition of non-resonant and resonant ROA bands of the chiral solvents. The unusual ROA enhancement was explained in terms of resonance energy transfer with resonant Raman emission. The surprising RROA sign-switching was found to be due to specific conformational equilibria where one solute conformer dominates in the ground and the other in the first excited singlet state, and, the signs of the related ECD bands of these two conformers are opposite.

Unusual solute to solvent induced chirality in ROA comes from specific conformer equilibria in the ground and the excited states.

Vibrational optical activity for structural characterization of natural products

This review presents the recent progress towards elucidating the structures of chiral natural products and applications using vibrational optical activity (VOA) spectroscopy.