Order Perturbation Theory Research Articles

Symmetry reduction, gauge reduction, backreaction, and consistent higher order perturbation theory

Symmetry reduction, gauge reduction, backreaction, and consistent higher order perturbation theory

A Case Study of an Energy Barrier in Li-Ion Battery Cathode Material Using DFT and Post-HF Approaches.

With the ever-increasing interest toward energy storage materials, an accurate understanding of the underlying physicochemical processes becomes mandatory for enabling accurate and predictive simulations. In this study, we apply multilevel quantum chemical calculations on a benchmark material commonly adopted as a cathode in Lithium batteries, Li0.5Co0.5+3Ni0.5+4O2. We estimate the Lithium hopping barrier, a key quantity for the estimate of Li diffusion coefficient, at different levels: Hartree-Fock (HF), density functional theory (DFT), periodic local Møller-Plesset perturbation theory of second order, complemented with a coupled cluster correction evaluated using an embedded-fragment approach. The post-HF methods were used here not only for benchmarking the key quantities themselves but also for assessing the accuracy of different functionals and probing the influence of the long-range and static correlation. For the given system and quantity in question, we observe that obtained results do not significantly vary across different DFT functionals or post-HF methods, which is rather uncommon. Such an agreement between the employed methods suggests that static correlation, even if prominent in this system, cancels out in the studied energy differences. In fact, the values of the T1 diagnostics, which test the reliability of the single-reference description, do vary from one fragment to another. But for certain fragments they are fairly small and of similar magnitude, indicating the applicability of such fragments for the correction. Our best estimate of the reaction barrier is about 0.85 eV.

Gas phase proton affinities of proline-containing peptides. 1: ProGly, ProAla, ProVal, ProLeu, ProIle, and ProPro

The gas-phase proton affinities (PA) for a series of proline-containing dipeptides have been measured in an ESI triple quadrupole instrument using the extended kinetic method. Proton affinities for ProGly (1), ProAla (2), ProVal (3), ProLeu (4), ProIle (5), and ProPro (6) were determined to be 969.6 ± 7.8, 990.4 ± 7.7, 987.6 ± 7.9, 982.8 ± 8.0, 988.8 ± 10.1, and 996.5 ± 12.2 kJ/mol, respectively. Predictions for the proton affinities for 1–6 were also obtained through isodesmic calculations at the B3LYP/6-311++G(d,p)//B3LYP/6-31+G(d) level of theory. The predicted proton affinities for 1 and 6 of 966.9 and 991.0 kJ/mol are in agreement with the experimental values. However, the predicted proton affinities for 2–5 of 973.5, 975.9, 975.7, and 975.9 are between 8 and 15 kJ/mol lower than the experimental values. Additional calculations with a larger basis set (B3LYP/6-311++G(2df,2p), inclusion of dispersion (B3LYP-D3/6-311++G(d,p)), switching to second order perturbation theory (MP2/6-31++G(d,p) and MP2/6-311++G(2df,2p), or switching density functional (M06-2x/6-311++G(d,p) and M06-2x/6-311++G(2df,2p) show only modest changes in derived thermochemistry lending support to the original calculations. We recommend using the experimental proton affinities for ProGly and ProPro and using the calculated values for ProAla, ProVal, ProLeu, and ProIle with the experimental proton affinities as upper limits.

High precision accelerator for our hybrid model of the redshift space power spectrum

Abstract Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modelling these statistics may require theoretical templates that go beyond two-loop order perturbation theory, especially for achieving precision at smaller scales. In our previous work, we introduced a hybrid model for the redshift space power spectrum of galaxies. This model combines two-loop order templates with N-body simulations to capture the influence of scale-independent parameters on the galaxy power spectrum. However, the impact of scale-dependent parameters was addressed by precomputing a set of input statistics derived from computationally expensive N-body simulations. As a result, exploring the scale-dependent parameter space was not feasible in this approach. To address this challenge, we present an accelerated methodology that utilizes Gaussian processes, a machine learning technique, to emulate these input statistics. Our emulators exhibit remarkable accuracy, achieving reliable results with just 13 N-body simulations for training. Our emulators can reproduce the set of statistics we are interested in with less than 0.1% error in the parameter space within 5σ of the Planck ΛCDM predictions, specifically for scales around k > 0.1 h Mpc−1. Following the training of our emulators, we can predict all inputs for our hybrid model in approximately 0.2 seconds at a specified redshift. Given that performing 13 N-body simulations is a manageable task, our present methodology enables us to construct efficient and highly accurate models of the galaxy power spectra within a manageable time frame.

Analysis of an iterative reconstruction method in comparison of the standard reconstruction method

ABSTRACT We present a detailed analysis of a new iterative density reconstruction algorithm. This algorithm uses a decreasing smoothing scale to better reconstruct the density field in Lagrangian space. We implement this algorithm to run on the quijote simulations, and extend it to (a) include a smoothing kernel that smoothly goes from anisotropic to isotropic, and (b) a variant that does not correct for redshift space distortions. We compare the performance of this algorithm with the standard reconstruction method. Our examinations of the methods include cross-correlation of the reconstructed density field with the linear density field, reconstructed two-point functions, and BAO parameter fitting. We also examine the impact of various parameters, such as smoothing scale, anisotropic smoothing, tracer type/bias, and the inclusion of second order perturbation theory. We find that the two reconstruction algorithms are comparable in most of the areas we examine. In particular, both algorithms give consistent fittings of BAO parameters. The fits are robust over a range of smoothing scales. We find the iterative algorithm is significantly better at removing redshift space distortions. The new algorithm will be a promising method to be employed in the ongoing and future large-scale structure surveys.

Second order perturbation theory of two-scale systems in fluid dynamics

In the present paper we study fast-slow systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. We prove that, under a suitable limit of infinite separation of scales, the slow component of the system converges in law to a solution of the initial equation perturbed by transport noise, and subject to the influence of an additional Itô–Stokes drift. The resulting limit equation is very similar to turbulent models derived heuristically. Our results apply to the Navier–Stokes equations in dimensions d=2,3 ; the surface quasi-geostrophic equations in dimension d=2 ; and the primitive equations in dimensions d=2,3 .

Quantum circuit for high order perturbation theory corrections

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for alternatives to classical methods. Recently, a general quantum circuit estimating the low order PT corrections has been proposed. In this article, we revisit the quantum circuits for PT calculations, and develop the methods for higher order PT corrections of eigenenergy, especially the 3rd and 4th order corrections. We present the feasible quantum circuit to estimate each term in these PT corrections. There are two the fundamental operations in the proposed circuit. One approximates the perturbation terms, the other approximates the inverse of unperturbed energy difference. The proposed method can be generalized to higher order PT corrections.

The direct role of nuclear motion in spin-orbit coupling in strongly correlated spin systems.

The interaction between the magnetic moment of an electron and the magnetic field generated by a moving charge is one component of the spin-orbit interaction. The nuclei in a molecule or solid are charged, are generally in vibrational motion, and so contribute to this interaction, but the direct coupling between nuclear momentum and electron spin is normally ignored in discussions of spin-forbidden phenomena such as transitions between states of different spin, even when the nuclei are recognized as playing a fundamental role (spin-vibronic coupling). Here, we investigate the spin-orbit interaction in a Heisenberg model interacting with vibrating point charges representing nearby bridging ligands. To reach the model, we apply second order perturbation theory to the Hubbard model with the spin-orbit interaction. In contrast to the other components of the spin-orbit interaction, the part that directly couples the momentum of the charge and electron spin appears at first order as an effective magnetic field at each site. We find that the inclusion of this nuclear-motion induced spin-orbit coupling can increase the rate of otherwise spin-forbidden transitions between different spin states of the Heisenberg model by many orders of magnitude. This overlooked interaction may, therefore, play a significant role in spin-forbidden phenomena such as spin relaxation in coupled spin-qubits.

The photodissociation dynamics and ultrafast electron diffraction image of cyclobutanone from the surface hopping dynamics simulation

The comprehension of nonadiabatic dynamics in polyatomic systems relies heavily on the simultaneous advancements in theoretical and experimental domains. The gas-phase ultrafast electron diffraction (UED) technique has attracted significant attention as a unique tool for monitoring photochemical and photophysical processes at the all-atomic level with high temporal and spatial resolutions. In this work, we simulate the UED spectra of cyclobutanone using the trajectory surface hopping method at the extended multi-state complete active space second order perturbation theory (XMS-CASPT2) level and thereby predict the results of the upcoming UED experiments in the Stanford Linear Accelerator Laboratory. The simulated results demonstrate that a few pathways, including the C2 and C3 dissociation channels, as well as the ring opening channel, play important roles in the nonadiabatic reactions of cyclobutanone. We demonstrate that the simulated UED signal can be directly interpreted in terms of atomic motions, which provides a unique way of monitoring the evolution of the molecular structure in real time. Our work not only provides numerical data that help to determine the accuracy of the well-known surface hopping dynamics at the high XMS-CASPT2 electronic-structure level but also facilitates the understanding of the microscopic mechanisms of the photoinduced reactions in cyclobutanone.

Modeling the BAO feature in bispectrum

Abstract We investigate how well a simple leading order perturbation theory model of the bispectrum can fit the BAO feature in the measured bispectrum monopole of galaxies. Previous works showed that perturbative models of the galaxy bispectrum start failing at the wavenumbers of k ∼ 0.1h Mpc−1. We show that when the BAO feature in the bispectrum is separated it can be successfully modeled up to much higher wavenumbers. We validate our modeling on GLAM simulations that were run with and without the BAO feature in the initial conditions. We also quantify the amount of systematic error due to BAO template being offset from the true cosmology. We find that the systematic errors do not exceed 0.3 per cent for reasonable deviations of up to 3 per cent from the true value of the sound horizon.

INELASTIC LONGITUDINAL C6 ELECTRON SCATTERING FORM FACTORS IN Ti-50, (RESIDUAL INTERACTION CONSIDERATION)

The single orbit 1f7/2 has been adopted as a model space. The use of modern realistic M3Y effective nucleon- nucleon interaction with two sets of fitting parameters (Ried fitting (M3Y-P1), and Paris fitting (M3Y-P0)) beside the use of MSDI has been done as a residual interactions within the calculation of core polarization effects in Inelastic longitudinal electron scattering C6 form factor in Ti-50 within the framework of first order perturbation theory (microscopic theory) with 2ћω excitation energy coupling the core orbits to the higher configurations one across the model space at normal transition. Harmonic oscillator wave functions (H.O) has been adopted as a single particle wave functions in 1f7/2 and with the aid of F7MBZ model space 1f7/2 effective interaction to generate the model space wave functions. The present results have been compared with

Estimating Baryon Density through the CAMB and Assessing its Reliability

The Cosmic Microwave Background Radiation and its anisotropies allow us to analyze many properties and phenomena of the early universe. One such important property is the Baryon Density(Ω_b), a cosmological constant for the density of Baryons in the universe in comparison to its critical density. Baryon Density affects the interactions of matter in the early universe and therefore the analysis of CMB Anisotropies to study how matter interacts allows for the estimation of the Baryon Density in the Early Universe. Understanding Ω_b, is crucial as it reveals information about the composition of the universe, such as the amount of dark matter and dark energy, the early formation of celestial bodies and matter-antimatter asymmetry. This paper aimed to test the reliability of CAMB, a simulation algorithm for CMB anisotropies, by estimating Ω_b h^2. The CAMB mainly utilizes a combination of field equations, the Friedmann-Lemaître-Robertson-Walker metric, Fluid Equations, the Boltzmann Equation and Linear Perturbation theory in order to compute the CMB power spectra. We estimated the value of Ω_b h^2, maintaining other cosmological parameters constant and changing Ω_b h^2 from 0.01 to 0.03 in increments of 0.000625. The peaks, troughs, positions, damping scale and amplitudes of the resultant TT and TE power spectra were compared with data from the Planck Satellite. We use chi-square minimization and find the best fit value and uncertainty forΩ_b h^2 to be 0.02325 ± 0.00015. The estimated value of the baryon density from our study was compared to existing estimates to evaluate the reliability of CAMB as a simulation and source of information for further CMB Anisotropy related research, where it was confirmed to be accurate. However, further developments using wider sets of data was acknowledged with deep learning being a potential step forward.

PROBING THE NUCLEAR STRUCTURE OF EXOTIC 33Mg ISOTOPE

Research on the nuclear structure of exotic isotopes, such as 33Mg, is an exciting and cuttingedge field of nuclear physics. Exotic isotopes are typically those that are far from the stable region of the nuclear chart and often exhibit unique properties that can help us better understand the fundamental forces and structure of atomic nuclei. In this paper the largescale shell model calculations are performed within the model spaces SDPFMU, to study the positive- and negative-parity energy levels and electromagnetic transitions in the exotic 33Mg isotope. Core-polarization effects on reduced transition probability are introduced through first order perturbation theory, which allows for higher energy configurations through excitations of nucleons from core orbits to that outside model space up to . The corepolarization effects have been improved the agreement of B(E2) with their corresponding experimental data, and have ignorable effect on B(M1)

Theory of electronic structure and effective masses of ultra-wide bandgap wurtzite aluminum nitride

I develop a theory of electronic structure for wurtzite(W)-Aluminium Nitride, based on the three uppermost valence bands and the lowest conduction band at the Γ-point. As distinguished from the Chuang-Chang approach [9], where the Hamiltonian is diagonalised considering all the bands, through an matrix, I follow a different procedure. In my approach, initially I follow a two-band approximation for the matrix, where the Hamiltonian is diagonalised by treating the conduction band and each of the valence bands separately. Thus, I diagonalise three different matrices, for obtaining the dispersions of the valence bands. The conduction band energy is obtained from the first diagonalization, involving band edge states. Effect of other two valence bands on a given valence band is considered through second order perturbation theory. Details of this procedure are outlined in Appendix A. It gives analytic expressions for the dispersion of the bands. I compare the results obtained for W-AlN with recent calculations and note satisfactory agreements. I also calculate the effective masses of holes in the valence bands both at the Γ-point and also as functions of the wavevector. My results agree fairly well with a recent calculation [3]. The hole effective masses for all the bands show large anisotropy. The effective mass of the electron in the conduction band does not show appreciable anisotropy.

Grazing incidence fast atom diffraction: general considerations, semiclassical perturbation theory and experimental implications.

Using semiclassical methods, an analytical approach to describe grazing incidence scattering of fast atoms (GIFAD) from surfaces is described. First, we consider a model with a surface corrugated in the scattering plane, which includes the surface normal and the incidence direction. The treatment uses a realistic, Morse potential, within a perturbation approach, and correctly reproduces the basic GIFAD phenomenology, whereby the scattering is directed primarily in the specular direction. Second, we treat the more general case of scattering from a surface corrugated in two-dimensions. Using time averaging along the direction of fast motion in the incidence direction, we derive a time dependent potential for the GIFAD scattering away from a low index direction. The results correctly describe the observation that diffraction is seen only when the scattering plane is aligned close to a low-index direction in the surface plane. For the case of helium scattering from LiF(001) we demonstrate that the resulting theoretical predictions agree well with experiment and show that the analysis provides new information on the scattering time and the length scale of the interaction. The analysis also gives insights into the validity of the axial surface channeling approximation (ASCA) and shows that within first order perturbation theory, along a low-index direction, the full 3-dimensional problem can be represented accurately by an equivalent 2-dimensional problem with a potential averaged along the third dimension. In contrast, away from low-index directions, the effective 2-dimensional potential in the projectile frame is time-dependent.

The random thermo-elastic nonlinear vibration analysis of porous FGM nano-beams using the first order perturbation theory

The objective of present work is to study the nonlocal nonlinear thermo-elastic vibrations of porous nanobeams made up of functionally graded material (FGM) with random material properties. The mechanical properties of the nano-beam are calculated using a porosity based power law model by assuming the cosine type porosity distributions. The randomness present in the material properties cause the mechanical characteristics of the nano-beams to be random, hence first order perturbation theory has been employed to take care of this randomness. The Reddy’s beam theory in association with the Eringen’s non classical elasticity has been used to account for nonlocal effects, and Von-karman nonlinearity has been employed to take care of geometric nonlinearity. The governing equations are derived from the minimum potential energy principle and solved them using the finite element method. To validate the present model, a convergence and comparison study has been performed. Further, the effects of amplitude ratio, aspect ratio, uncertain material properties, size parameter, porosity, thermal environment, and gradation of material on the stochastic behavior of the porous FGM nano-beams are demonstrated. As a result of the present research, the significance of considering thermal environment, porosity, and random material properties has been revealed for the design of nanodevices and systems to be more reliable.

Internal conversion as second order process with electric dipole operator

Classical consideration of internal conversion (IC) is one step process with the nonadiabatic coupled operator within the first order perturbation theory between the initial and final electronic states. We suggest considering the IC as the second order two step process with the electric dipole operator (d). Within this approximation the initial state is excited electronic state and the final one is the ground electronic state. The electronic excited energy in converted into the excitation of C-C bonds with the virtual photon emission at the first step. After that the virtual photon is absorbed by X-H (X = C, N and O) bonds. This mechanism can be important for the influence of external field on the IC process, too. It is called the induced effect. Estimation of two step process with d operator for two compounds: Azatrioxa[8]circulene (ATOC) and heptamethine cyanine (IR808) shows that this effect is noticeable when the external electric field is about 108 V/m - 109 V/m and the energy gap between the initial and final electronic states is about 10000–12000 cm−1.

Introducing the embedded random phase approximation: H2 dissociative adsorption on Cu(111) as an exemplar

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. We explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078–7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208–3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

When do tripdoublet states fluoresce? A theoretical study of copper(II) porphyrin.

Open-shell molecules rarely fluoresce, due to their typically faster non-radiative relaxation rates compared to closed-shell ones. Even rarer is the fluorescence from states that have two more unpaired electrons than the open-shell ground state, since they involve excitations from closed-shell orbitals to vacant-shell orbitals, which are typically higher in energy compared to excitations from or out of open-shell orbitals. States that are dominated by the former type of excitations are known as tripdoublet states when they can be described as a triplet excitation antiferromagnetically coupled to a doublet state, and their description by unrestricted single-reference methods (e.g., U-TDDFT) is notoriously inaccurate due to large spin contamination. In this work, we applied our spin-adapted TDDFT method, X-TDDFT, and the efficient and accurate static-dynamic-static second order perturbation theory (SDSPT2), to the study of the excited states as well as their relaxation pathways of copper(II) porphyrin; previous experimental works suggested that the photoluminescence of some substituted copper(II) porphyrins originate from a tripdoublet state, formed by a triplet ligand π → π* excitation antiferromagnetically coupled with the unpaired d electron. Our results demonstrated favorable agreement between the X-TDDFT, SDSPT2 and experimental excitation energies, and revealed noticeable improvements of X-TDDFT compared to U-TDDFT, not only for vertical excitation energies but also for adiabatic energy differences. These suggest that X-TDDFT is a reliable tool for the study of tripdoublet state fluorescence. Intriguingly, we showed that the aforementioned tripdoublet state is only slightly above the lowest doublet excited state and lies only slightly higher than the lowest quartet state, which suggests that the tripdoublet of copper(II) porphyrin is long-lived enough to fluoresce due to a lack of efficient non-radiative relaxation pathways; an explanation for this unusual state ordering is given. Indeed, thermal vibration correlation function (TVCF)-based calculations of internal conversion, intersystem crossing, and radiative transition rates confirm that copper(II) porphyrin emits thermally activated delayed fluorescence (TADF) and a small amount of phosphorescence at low temperature (83K), in accordance with experiment. The present contribution is concluded by a few possible approaches of designing new molecules that fluoresce from tripdoublet states.

WIMP decay as a possible Warm Dark Matter model

Abstract The Weakly Interacting Massive Particles (WIMPs) have long been the favoured Cold Dark Matter (CDM) candidate in the standard ΛCDM model. However, owing to great improvement in the experimental sensitivity in the past decade, some parameter space of the Supersymmetric (SUSY)-based WIMP model is ruled out. In addition, a massive stable WIMP as the CDM particle is also at variance with other astrophysical observables at small scales. We consider a model that addresses both these issues. In the model, the WIMP decays into a massive particle and radiation. We study the background evolution and the first order perturbation theory (coupled Einstein-Boltzmann equations) for this model and show that the dynamics can be captured by a single parameter r = mL/q, which is the ratio of the lighter mass and the comoving momentum of the decay particle. We incorporate the relevant equations in the existing Boltzmann code CLASS to compute the matter power spectra and Cosmic Microwave Background (CMB) angular power spectra. The decaying WIMP model is akin to a non-thermal Warm Dark Matter (WDM) model and suppresses matter power at small scales, which could alleviate several issues that plague the CDM model at small scales. We compare the predictions of the model with CMB and galaxy clustering data. As the model deviates from the ΛCDM model at small scales, the evolution of the collapse fraction of matter in the universe is compared with the high-redshift Sloan Digital Sky Survey (SDSS) HI data. Both these data sets yield r ≳ 106, which can be translated into the bounds on other parameters. In particular, we obtain the following lower bounds on the thermally-averaged self-annihilation cross-section of WIMPs, ⟨σv⟩, and the lighter mass: ⟨σv⟩ ≳ 4.9 × 10-34 cm3 sec-1 and mL ≳ 2.4 keV. The lower limit on mL is comparable to constraints on the mass of thermally-produced WDM particle. The limit on the self-annihilation cross-section greatly expands the available parameter space as compared to the stable WIMP scenario.