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

Abstract

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.

The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory

“…A first step toward this direction can be found in ref for FDE in combination with ADC(2). Alternatively, higher-order response contributions can be incorporated by means of, for example, real-time sTDDFT. , Recently, the usage of such techniques for finite and extended molecular systems has gained momentum. ,− …”

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

“…For further details on the derivation, as well as the extension to arbitrary unit cell shapes, we refer to the literature. 16,41 The expressions derived by the modern theory of polarization are routinely applied to calculate the expectation value of the bulk polarization, for example in calculations of Raman spectra, 17,32,[42][43][44] Born effective charges and IR spectra, 13,[45][46][47][48][49] ferroelectric materials, 46,[50][51][52][53] piezoelectricity, [54][55][56] dielectric constants, 47,57 the (anomalous) Hall effect, 58,59 magnetoelectric responses, 60 and sum frequency generation spectra. 34,35 As pointed out e.g.…”

“…In this way, the total expectation value can be partitioned into contributions from each center, or groups of Wannier centers centered around individual bonds and atoms, functional groups, or molecules. This approach is not limited to periodic systems and has been applied to IR spectra, 23,49,[72][73][74][75][76][77][78][79] VCD spectra calculations, 80 Raman spectra calculations, 32,74,81 ROA spectra calculations, 33 SFG spectra calculations, 34,[82][83][84] high harmonic generation in crystals, 85 Hall conductivities, 86,87 the magnetoelectric polarizability tensor, 88 Magnetic Circular Dichroism (MCD) spectra 89 of ferroelectrics, 90 piezoelectric constants, 56 the shift-current response in piezoelectric crystals, 91 and dielectric constants. 76,77,92 MLWFs have not only been used to calculate the bulk polarization and molecular polarizabilities, but have been also applied to magnetic properties.…”

“…Although hybrid exchange-correlation functionals, including a fraction of exact Hartree-Fock exchange, could be applied, this has not been done so far for the NVPT. The solutions of eqn (49) are the KS-MO coefficients C j for the jth KS orbital (f j ) from which the real space electron density n(r) is calculated as…”

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

“…With regard to simulating the response of the laser pulses relevant to pump–probe spectroscopies, the real-time (RT) formalism offers a straightforward approach − over response-theory-based methods as the former is applicable for a large range of field intensities and resembles the experimental setup in a natural way. Addressing core-level spectroscopies has added complexities, as it requires the inclusion of scalar (SC) and spin–orbit (SO) relativistic effects, which are most reliably described by multicomponent relativistic quantum chemical methods.…”