Frequency-dependent Polarizabilities Research Articles

TDDFT Investigation of the Raman and Resonant Raman Spectra of Fluorescent Protein Chromophore Models.

The off-resonance and resonant Raman spectra have been simulated for models of fluorescent protein chromophores, those of the green fluorescent protein (GFP, called FP1) and of DsRed (called FP2), which presents a longer π-conjugated path, with the aim of providing a systematic investigation of structural but also computational aspects. These were performed at the (time-dependent) density functional theory [(TD)DFT] level. The off-resonance intensities have been calculated from the derivatives of the frequency-dependent polarizability with respect to the normal coordinates while the resonant ones have been evaluated using Huang-Rhys factors determined from the gradients of the excitation energies with respect to the normal coordinates. When applied with the M05 meta-GGA exchange-correlation functional, this simple computational scheme can reproduce most of the experimental Raman signatures of FP1 in its protonated and deprotonated forms, the differences of vibrational signatures of the cis (Z) and trans (E) isomers, as well as their changes as a function of the excitation wavelength. On the other hand, testing the predictions made for FP2 would require new experimental work. It was also observed that simulations with methods that inadequately predict the resonant Raman spectra could nevertheless produce a UV-vis absorption spectrum that is quite similar to the one obtained with better methods, once realistic peak broadening has been applied.

Linear and Nonlinear Optical Properties from TDOMP2 Theory

We present a derivation of real-time (RT) time-dependent orbital-optimized Møller–Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

Ground-state frequency-dependent dipole polarizabilities of [formula omitted] three-electron ions

Frequency-dependent dipole polarizabilities of 22S lithiumlike states for 3≤Z≤10 are tabulated for frequencies up to the 32P absorption frequency using fully correlated Gaussian expansions. To account for the frequency-dependence between and near the poles at the 22P and 32P absorption frequencies, the Schrödinger–Coulomb Hamiltonian is diagonalized in a composite basis of L=1 angular momentum Gaussians containing subsets of partially optimized n2P (n=2−5) wavefunctions and both frequency-independent and frequency-dependent first-order perturbed functions. The tabulated results are well-converged and should be considered as benchmark dipole polarizabilities in the non-relativistic limit. The calculated dipole polarizabilities are used to determine a fit to the Cauchy expansion. The 32P and 42P energies calculated using the composite basis set are new upper bounds to the exact non-relativistic energies, as are many of the 52P energies.

Optical and magneto-optical properties of ferromagnetic monolayer CrBr3 : A first-principles GW and GW plus Bethe-Salpeter equation study

The discovery of atomically thin two-dimensional (2D) magnetic semiconductors has triggered enormous research interest recently. In this work, we use first-principles many-body perturbation theory to study a prototypical 2D ferromagnetic semiconductor, monolayer chromium tribromide (CrBr$_3$). With broken time-reversal symmetry, spin-orbit coupling, and excitonic effects included through the full-spinor $GW$ and $GW$ plus Bethe-Salpeter equation ($GW$-BSE) methods, we compute the frequency-dependent layer polarizability tensor and dielectric function tensor that govern the optical and magneto-optical properties. In addition, we provide a detailed theoretical formalism for simulating magnetic circular dichroism, magneto-optical Kerr effect, and Faraday effect, demonstrating the approach with monolayer CrBr$_3$. Due to reduced dielectric screening in 2D and the localized nature of the Cr $d$ orbitals, we find strong self-energy effects on the quasiparticle band structure of monolayer CrBr$_3$ that give a 3.8 eV indirect band gap. Also, excitonic effects dominate the low-energy optical and magneto-optical responses in monolayer CrBr$_3$ where a large exciton binding energy of 2.3 eV is found for the lowest bright exciton state with excitation energy at 1.5 eV. We further find that the magneto-optical signals demonstrate strong dependence on the excitation frequency and substrate refractive index. Our theoretical framework for modeling optical and magneto-optical effects could serve as a powerful theoretical tool for future study of optoelectronic and spintronics devices consisting of van der Waals 2D magnets.

Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method

In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.

Measurement of the tune-out wavelength for Cs133 at 880 nm

We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the ${D}_{1}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and ${D}_{2}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for $^{133}\mathrm{Cs}$ in the ground hyperfine state $(F=3,{m}_{F}=+3)$. At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a $^{133}\mathrm{Cs}$ Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

Crystal structure elucidation, experimental and computational optical properties of novel acceptor-donor-acceptor organic material: A suitable candidate for nonlinear applications

A new organic nonlinear optical (NLO) material, 2-(4-chlorophenoxy)-N'-[(1E)-1-(4-fluorophenyl) ethylidene] acetohydrazide (4CP4FPEA), has been synthesized and single crystals were grown using DMF as solvent. The compound was characterized by 1H NMR and single X-ray diffraction analyses. Analysis of intermolecular interactions was carried out by mapping Hirshfeld surfaces over 2D fingerprint plots, dnorm and curvedness using Crystal Explorer. Open aperture Z-Scan experimental curve showed that the 4CP4FPEA molecule exhibits lower transmittance at the focus at 532 nm wavelength. 4CP4FPEA exhibits good optical limiting behavior at the wavelength 532 nm. Estimated excited state absorption cross-section (σex) and ground state absorption cross-section (σg) are found to be 3.59 × 10−17cm2 and 1.9 × 10−21 cm2 respectively (σg <<< σex) indicating that nonlinear absorption is due to Reverse Saturable Absorption. Semi-empirical calculations were implemented to calculate static and frequency dependent mean polarizability, first-order hyperpolarizability and second-order hyperpolarizability using time-dependent Hartree–Fock (TDHF) method. We have observed enhancement in nonlinear optical property compared to our previous reported molecule 2-(4-chlorophenoxy)-N'-[(1E)-1-(4-methylphenyl) ethylidene] acetohydrazide (4CP4MPEA).

Investigating functional performance and substituent effect in modelling molecular structure, UV-visible spectra, and optical properties of D-π-A conjugated organic dye molecules: a DFT and TD-DFT study

The molecular structure, UV-visible spectra, and optical properties of D-π-A conjugated organic dye molecules (Disperse Red 1 (DR1) and Disperse Red 73 (DR73)) were analyzed using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) and compared with azobenzene molecule to study the effect of donor and acceptor substituents on the molecular properties. The performance of DFT functionals is investigated using B3LYP hybrid functional and three long-range corrected functionals (CAM-B3LYP, LC-ω PBE, and ω B97XD) in conjunction with 6-31G(d,p) basis set. Using TD-DFT, we calculate the vertical excitation energies and transition dipole moment values for 100 excited states. These values were further utilized to calculate frequency dependent polarizability under sum-over-states (SOS) formalism and refractive index of these molecular systems. We observe that for azobenzene and DR1 molecules, ω B97XD predicted wavelengths corresponding to peak absorbance closest to the experimental results, while for DR73 molecule, B3LYP gave better prediction. Large polarizability response is also observed for these molecules (DR1 and DR73) in comparison to parent azobenzene structure due to charge transfer between donor and acceptor groups. For DR1 and DR73 molecules, αxx component of polarizability dominates in contrast to azobenzene where αyy dominates. The HOMO → LUMO transition during excitation contributes to the peak molecular response in simulated UV-visible spectra. The high polarizability response of selected D-π-A conjugated molecules in comparison to parent molecule suggests that these molecules are promising candidates for tailor-made photonic and optoelectronic device development. Graphical Abstract Functional and substituent effect on the optical response of D-π-A conjugated molecules modelled using DFT and TDDFT.

Dynamical polarizability of graphene with spatial dispersion

We perform a detailed analysis of electronic polarizability of graphene with different theoretical approaches. From Kubo's linear response formalism, we give a general expression of frequency and wave-vector dependent polarizability within the random phase approximation. Four theoretical approaches have been applied to the single-layer graphene and their differences are on the band-overlap of wavefunctions. By comparing with the \textit{ab initio} calculation, we discuss the validity of methods used in literature. Our results show that the tight-binding method is as good as the time-demanding \textit{ab initio} approach in calculating the polarizability of graphene. Moreover, due to the special Dirac-cone band structure of graphene, the Dirac model reproduces results of the tight-binding method for energy smaller than \SI{3}{\electronvolt}. For doped graphene, the intra-band transitions dominate at low energies and can be described by the Lindhard formula for two-dimensional electron gases. At zero temperature and long-wavelength limit, with the relaxation time approximation, all theoretical methods reduce to a long-wave analytical formula and the intra-band contributions agree to the Drude polarizability of graphene. Effects of electrical doping and temperature are also discussed. This work may provide a solid reference for researches and applications of the screening effect of graphene.

Size-dependent polarizabilities and van der Waals dispersion coefficients of fullerenes from large-scale complex polarization propagator calculations.

While the anomalous non-additive size-dependencies of static dipole polarizabilities and van der Waals C6 dispersion coefficients of carbon fullerenes are well established, the widespread reported scalings for the latter (ranging from N2.2 to N2.8) call for a comprehensive first-principles investigation. With a highly efficient implementation of the linear complex polarization propagator, we have performed Hartree-Fock and Kohn-Sham density functional theory calculations of the frequency-dependent polarizabilities for fullerenes consisting of up to 540 carbon atoms. Our results for the static polarizabilities and C6 coefficients show scalings of N1.2 and N2.2, respectively, thereby deviating significantly from the previously reported values obtained with the use of semi-classical/empirical methods. Arguably, our reported values are the most accurate to date as they represent the first ab initio or first-principles treatment of fullerenes up to a convincing system size.

Plasmon effects in the two-photon Rabi oscillations in a strongly coupled semiconductor quantum dot–metal nanoshell composite

We theoretically study two-photon Rabi oscillations (TPRO) in a nanocomposite comprising a semiconductor quantum dot (SQD) strongly coupled to a metallic nanoshell (MNS), which undergoes a pulsed excitation. The SQD is modeled as a three-level ladder-like quantum system (ground, one-exciton, and bi-exciton states). Its optical dynamics is described quantum-mechanically within the density matrix formalism framework, while the MNS is treated classically through its frequency-dependent polarizability. We find two effects of the presence of a MNS in close proximity to the SQD: (a) - a sufficient increase of the number of Rabi cycles as compared to the case of an isolated SQD and (b) - incoherent population of the one-exciton state giving rise to the destruction of the TPRO.

Electron confinement meet electron delocalization: non-additivity and finite-size effects in the polarizabilities and dispersion coefficients of the fullerenes.

In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (αl with l = 1, 2, 3) for the C60-C84 fullerenes and quantitatively assess the intrinsic non-additivity in these fundamental response properties. By comparing against classical models of the fullerenes as conducting spherical shells (or solid spheres) of uniform electron density, a detailed critical analysis of the derived effective scaling laws (α1 ∼ N1.2, α2 ∼ N2.0, α3 ∼ N2.7) demonstrates that the electronic structure of finite-sized fullerenes-a unique dichotomy of electron confinement and delocalization effects due to their quasi-spherical cage-like structures and encapsulated void spaces-simultaneously limits and enhances their quantum mechanical response to electric field perturbations. Corresponding frequency-dependent polarizabilities were obtained by inputting the αl series into the hollow sphere model (within the modified single frequency approximation), and used to compute the molecular dispersion coefficients (Cn with n = 6, 8, 9, 10) needed to describe the non-trivial van der Waals (vdW) interactions in fullerene-based systems. Using first-order perturbation theory in conjunction with >140 000 DFT calculations, we also computed the non-negligible zero-point vibrational contributions to α1 in C60 and C70, thereby enabling a more accurate and direct comparison between theory and experiment for these quintessential nanostructures.

Динамическая поляризуемость отрицательного иона водорода

We performed the calculations of the frequency-dependent polarizability of a hydrogen anion by using correlation-consistent basis sets with high diffuseness. The results obtained turned out to be close to the results obtained by the method of summation over pseudo-states. It is also shown that calculations by the density functional method do not allow obtaining high accuracy. This is due to the large size of anions compared to both cations and neutral atoms (molecules).

TD-DFT Studies on sp- and sp2-Hybridized Single Vacancy-Defected [60]Fullerene: Electronic Excitation and Nonlinear Optical Properties of C59 [9-4] and C59 [8-5] Isomers.

By removing one carbon atom from [60]Fullerene (C60), two different isomers (C59 [9-4] and C59 [8-5]) are generated for the C59 cluster. Inspired by their structural and electronic properties, we, theoretically, studied the static and frequency-dependent electronic (hyper)polarizabilities of sp- and sp2-hybridized isomers in vacuum by TD-DFT calculations. The simulated absorption spectra showed that all absorption bands of C59 [9-4] and C59 [8-5] are attributed to π → π* and n → π* transitions. Regarding their nonlinear optical properties, it is found that the frequency-dependent polarizability anisotropy αanisotropy(λ = 1064.80 nm) of C59 [8-5] is 4 times larger than the static regime, revealing a notable polarization anisotropy, due to the delocalized π electrons around the vacancy defect. By decreasing the incident wavelengths from λ = 1908 nm to λ =589.08 nm, the dispersion of optical nonlinearity of C59 [8-5] has achieved the maximum at βxxx (λ = 1064.8 nm) = 38.150 au and (γxxxx (λ = 589.08 nm) = -9.896 × 107 au), indicating that the resonance effect of the hyperpolarizability amplified with the decrease of incident wavelengths. Hyperpolarizability density analyses in X and Z directions displayed that the conspicuous negative ρxxx(3)(r⃗) and -zρzzz(3)(r⃗) are more expanded on the C59 [8-5] cage when the main contributions stem from the π electrons instead to the sp-hybridized carbon.

Vector polarizability of an atomic state induced by a linearly polarized vortex beam: External control of magic, tune-out wavelengths, and heteronuclear spin oscillations

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular-momentum conservation of the beam. The theory is employed on $^{87}\mathrm{Sr}^{+}$ to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using the relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes a fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and orbital angular momentum of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}\mathrm{Rb}$ and $^{23}\mathrm{Na}$ atoms.

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.

Frequency and water saturation dependency of dielectric properties of clay mineral

An investigation of the frequency dependent dielectric polarizability of water molecules bound to clay mineral surfaces using molecular dynamic simulation is essential to improve understanding of the bulk electrical transport properties of shales in petrophysics and other clay science. The aim of the present study was to quantify the frequency-dependence of the complex permittivity of K+-smectite partially and fully saturated with water and to determine the relaxation frequency of the K+-smectite for pore size of ~1 nm and smectite matrix basal space of 1.66 nm with water saturations that varied from 20 to 100 wt% using molecular dynamics simulations. The simulation results of the dielectric spectra showed an unchanged polarization mechanism occurring within the K+-smectite with nano pore size, characterized by a water saturation dependent static permittivity. The characteristic frequency of the dielectric relaxation was found to be ~30 GHz for the system studied. The permittivity relaxation was found to be non-Debye type relaxation, with a circular arc locus providing a good representation of the simulated data. The deviation from pure Debye behavior reduced and the dielectric permittivity became much more significant as water saturation increases. The results presented here identified the dielectric relaxation as resulting from the orientational correlation of the water molecules near the K+-smectite surface and gave support to the idea that the relaxation frequency reflects the dimension of pores. This work constituted a novel contribution to the dielectric spectra of overall wet K+-smectite by extending the dielectric behavior of the clay mineral-water system to a microscopic level description.

Monitoring the Physiological State in the Dark Fermentation of Maize/Grass Silage Using Flow Cytometry and Electrooptic Polarizability Measurements

Dark fermentation (DF), a key biohydrogen-producing process, is generally operated as a black-box, by monitoring different operative macroscopic process parameters without evaluating or tracking the physiology of the biotic phase. The biotic phase in DF is constituted by a large variety of microorganisms, mainly fermentative bacteria. The present study uses two (electro)optical techniques, flow cytometry (FC) and frequency-dependent polarizability anisotropy (FDPA) measurements, to gain insights into the physiology of open mixed consortia throughout the DF process. The mixed consortia for DF were obtained from a methanogenic sludge, selecting spore-forming bacteria by means of an acid treatment. Then, DF systems with and without pH control were studied, using as substrate a mixture of maize and grass silage (9:1 w/w). Over the course of fermentation, the butyric pathway was dominant in both systems, and relevant titers of acetate, formate, and ethanol were detected; while hydrogen yields amounted to 20.80 ± 0.05 and 17.08 ± 0.05 NmL/gVS under pH-regulated and non-regulated conditions, respectively. The cytometric pattern analysis of the culture together with microscopic observations made it possible, over the course of fermentation, to identify and track the predominant morphologies in play (i.e., free spore, rod-shaped, and endospore, which are typical of Clostridium spp.). Furthermore, the use of the fluorescent dye DiBAC4(3) in FC and FDPA measurements provided similar information regarding the physiological state (PS) of the mixed consortia during the different phases of the culture.Graphical

Complex excited state polarizabilities in the ADC/ISR framework.

We present the derivation and implementation of complex, frequency-dependent polarizabilities for excited states using the algebraic-diagrammatic construction for the polarization propagator (ADC) and its intermediate state representation. Based on the complex polarizability, we evaluate C6 dispersion coefficients for excited states. The methodology is implemented up to third order in perturbation theory in the Python-driven adcc toolkit for the development and application of ADC methods. We exemplify the approach using illustrative model systems and compare it to results from other ab initio methods and from experiments.

Benchmarking doubles-corrected random-phase approximation methods for frequency dependent polarizabilities: Aromatic molecules calculated at the RPA, HRPA, RPA(D), HRPA(D), and SOPPA levels.

The performance of different polarization propagator methods, such as RPA, RPA(D), HRPA, HRPA(D), and SOPPA, have been tested against CC3 values for both static and dynamic polarizabilities. The test set consists of 14 (hetero-)aromatic medium-sized organic molecules, mostly with a high degree of symmetry. The benchmark of the methods remarkably reveals that RPA and HRPA(D) yield results comparable with the CC3 values and that they outperform SOPPA for these molecules. For a subset of the molecules, a comparison could be made to experimental values. The comparison for static polarizabilities proves that RPA and HRPA(D) as well as RPA(D) reproduce experimental values to a satisfying precision, whereas the SOPPA method compared to these three methods appears to perform only adequately. An investigation of the performance of Sadlej's polarized triple zeta basis set against Dunning's aug-cc-pVTZ basis set was also carried out. It is found that in contrast to other methods, Sadlej's basis set did not perform sufficiently compared to the larger aug-cc-pVTZ basis set for the RPA based methods.