Third-order Perturbation Theory Research Articles

Resonant Raman in armchair graphene nanoribbons from first-principles

Resonant Raman spectra of armchair graphene nanoribbons (AGNRs) are computed using Density Functional Theory (DFT) and third-order perturbation theory. Results are benchmarked against available experimental data and compared to previously used theoretical approaches based on the Placzek approximation. Comparable agreement with experiments is found for both previously and presently used methods. In addition, a numerical analysis is carried out to provide a justification for the resonant modeling method based on the use of the frequency-dependent dielectric tensor in the Placzek approximation. This work also provides additional predictions and references for wide AGNRs that might be investigated with Raman scattering experiments in the future.

Second Wilson number from third-order perturbation theory for the symmetric single-impurity Kondo model at low temperatures

We determine the impurity-induced free energy and the impurity-induced zero-field susceptibility of the symmetric single-impurity Kondo model from weak-coupling perturbation theory up to third order in the Kondo coupling at low temperatures and small magnetic fields. We reproduce the analytical structure of the zero-field magnetic susceptibility as obtained from Wilson’s renormalization group method. This permits us to obtain analytically the first two Wilson numbers.

Thermodynamic properties of fluids with Mie n − m potentials and application to tune effective Mie potentials for simple real fluids

ABSTRACT Monte Carlo computer simulations have been performed to obtain the equation of state and internal energy of fluids with Mie n − m potentials, with m = 6 and n = 9, 12 and 15, for different supercritical temperatures and densities covering most of the fluid phase. These data have been used to test the performance of a third-order perturbation theory with the first three perturbation terms determined from computer simulation, giving rise to a very good agreement between theory and simulation. Next, the theory has been used to tune effective two-body Mie n − 6 potentials for the real fluids Ne, Ar, Kr, Xe and C H 4 at supercritical temperatures for wide range of densities and pressures. It has been shown that the theory is able to accurately fit the experimental data for the energy and pressure of these fluids within the temperature and density ranges considered. This theory might be useful to obtain the equation of state and the internal energy of real molecular fluids within the context of the SAFT-VR Mie theory.

Consistent third-order one-particle transition and excited-state properties within the algebraic-diagrammatic construction scheme for the polarization propagator.

The intermediate state representation (ISR) formalism allows for the straightforward calculation of excited state properties and state-to-state transition moments using the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator. Here, the derivation and implementation of the ISR in third-order perturbation theory for the one-particle operator are presented, enabling, for the first time, the calculation of consistent third-order ADC [ADC(3)] properties. The accuracy of ADC(3) properties is evaluated with respect to high-level reference data and compared to the previously used ADC(2) and ADC(3/2) schemes. Oscillator strengths and excited state dipole moments are computed, and typical response properties are considered: dipole polarizabilities, first-order hyperpolarizabilities, and two-photon absorption strengths. The consistent third-order treatment of the ISR leads to an accuracy similar to that of the mixed-order ADC(3/2) method; the individual performance, however, depends on the property and molecule under investigation. ADC(3) produces slightly improved results in the case of oscillator strengths and two-photon absorption strengths, while excited state dipole moments, dipole polarizabilities, and first-order hyperpolarizabilities exhibit similar accuracy at ADC(3) and ADC(3/2) levels. Taking the significant increase of central processing unit time and memory requirements of the consistent ADC(3) approach into account, the mixed-order ADC(3/2) scheme offers a better compromise between accuracy and efficiency for the properties considered.

Attosecond interferometry of neon atom: photoelectron angular distributions

In the paper we present the angular distributions of photoelectrons in ionization of neon atom by a field of several multiple frequencies. The considered setup is refered to the RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) spectroscopy under condition that the field frequencies are selected in such a way that resonant transitions through discrete states play an important role. The role of the phase of the seed infrared field on the angular distributions of photoemission is analyzed. A significant difference in the anisotropy parameters at the near-threshold sideband caused by transitions through discrete states is shown. Two methods are compared: numerical solution of rate equations with continuum discretization and third-order perturbation theory.

Quadratic Spin-Orbit Mechanism of the Electronic g-Tensor.

Understanding how the electronic g-tensor is linked to the electronic structure is desirable for the correct interpretation of electron paramagnetic resonance spectra. For heavy-element compounds with large spin-orbit (SO) effects, this is still not completely clear. We report our investigation of quadratic SO contributions to the g-shift in heavy transition metal complexes. We implemented third-order perturbation theory in order to analyze the contributions arising from frontier molecular spin orbitals (MSOs). We show that the dominant quadratic SO term─spin-Zeeman (SO2/SZ)─generally makes a negative contribution to the g-shift, irrespective of the particular electronic configuration or molecular symmetry. We further analyze how the SO2/SZ contribution adds to or subtracts from the linear orbital-Zeeman (SO/OZ) contribution to the individual principal components of the g-tensor. Our study suggests that the SO2/SZ mechanism decreases the anisotropy of the g-tensor in early transition metal complexes and increases it in late transition metal complexes. Finally, we apply MSO analysis to the investigation of g-tensor trends in a set of closely related Ir and Rh pincer complexes and evaluate the influence of different chemical factors (the nuclear charge of the central atom and the terminal ligand) on the magnitudes of the g-shifts. We expect our conclusions to aid the understanding of spectra in magnetic resonance investigations of heavy transition metal compounds.

Classical density functional theory for interfacial properties of hydrogen, helium, deuterium, neon, and their mixtures.

We present a classical density functional theory (DFT) for fluid mixtures that is based on a third-order thermodynamic perturbation theory of Feynman-Hibbs-corrected Mie potentials. The DFT is developed to study the interfacial properties of hydrogen, helium, neon, deuterium, and their mixtures, i.e., fluids that are strongly influenced by quantum effects at low temperatures. White Bear fundamental measure theory is used for the hard-sphere contribution of the Helmholtz energy functional, and a weighted density approximation is used for the dispersion contribution. For mixtures, a contribution is included to account for non-additivity in the Lorentz-Berthelot combination rule. Predictions of the radial distribution function from DFT are in excellent agreement with results from molecular simulations, both for pure components and mixtures. Above the normal boiling point and 5% below the critical temperature, the DFT yields surface tensions of neon, hydrogen, and deuterium with average deviations from experiments of 7.5%, 4.4%, and 1.8%, respectively. The surface tensions of hydrogen/deuterium, para-hydrogen/helium, deuterium/helium, and hydrogen/neon mixtures are reproduced with a mean absolute error of 5.4%, 8.1%, 1.3%, and 7.5%, respectively. The surface tensions are predicted with an excellent accuracy at temperatures above 20K. The poor accuracy below 20K is due to the inability of Feynman-Hibbs-corrected Mie potentials to represent the real fluid behavior at these conditions, motivating the development of new intermolecular potentials. This DFT can be leveraged in the future to study confined fluids and assess the performance of porous materials for hydrogen storage and transport.

First-principles study on the thermoelectric properties of Sr2Si and Sr2Ge

The development of environmentally friendly thermoelectric materials composed of earth-abundant, non-toxic elements is highly desirable in thermoelectric technology. In this study, the thermoelectric properties of n-type doped Sr2Si and Sr2Ge were systematically investigated using first-principles density functional theory calculations combined with semi-classical Boltzmann transport theory. The multi-band feature in the conduction band of Sr2Ge leads to a higher Seebeck coefficient than Sr2Si, resulting in a higher power factor. The phonon transport calculations using third-order perturbation theory predict ultra-low lattice thermal conductivity of 0.42 Wm−1K−1 for Sr2Si and 0.33 Wm−1K−1 for Sr2Ge at 900 K. The maximum figure of merit ZT is 1.44 for Sr2Ge, which is approximately 1.25 times higher than that of 1.15 for Sr2Si at 900 K. Our results indicate that the Sr2Ge and Sr2Si are promising candidates for high-performance thermoelectric materials.

Assessment of State-Averaged Driven Similarity Renormalization Group on Vertical Excitation Energies: Optimal Flow Parameters and Applications to Nucleobases.

We present a comprehensive excited-state benchmark for the state-averaged (SA) driven similarity renormalization group (DSRG) [Li, C.; Evangelista, F. A. J. Chem. Phys. 2018, 148, 124106]. Following the QUEST database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; Loos, P.-F. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2021, 11, e1517], 280 vertical transition energies of 35 medium-sized molecules are computed using the SA-DSRG derived second- and third-order perturbation theories (PT2/PT3) along with a nonperturbative approach [sq-LDSRG(2)]. Comparing to the theoretical best estimates, the optimal flow parameter is found to be 0.35 and 2.0 for SA-DSRG-PT2 and SA-DSRG-PT3, respectively. For SA-sq-LDSRG(2), a flow parameter of 1.5 provides converged equations without compromising the accuracy. We then assess the accuracy of the SA-DSRG hierarchy using these parameters. The SA-DSRG-PT2 scheme outperforms the level-shifted CASPT2 by 0.10 eV in mean absolute error (MAE), yet this accuracy is slightly inferior than that of CASPT2 with the ionization-potential-electron-affinity shift. Both SA-DSRG-PT3 and SA-sq-LDSRG(2) yield a MAE of 0.10 eV, which is comparable to that of CASPT3 (0.09 eV). Finally, we compute vertical excitation energies of several low-lying singlet states of nucleobases. The SA-sq-LDSRG(2) approach provides highly accurate results for π → π* excitations, while n → π* transitions are better described by SA-DSRG-PT3.

Thermodynamic properties of Ar, Kr and Xe from a Monte Carlo-based perturbation theory with an effective two-body Lennard-Jones potential

A third-order perturbation theory is used to obtain the equilibrium properties of Ar, Kr and Xe over wide ranges of temperatures and densities. The theory belongs to the framework of the inverse temperature expansion of the Helmholtz free energy, with the perturbation terms determined from Monte Carlo simulation. The interactions are modeled by an effective two-body Lennard-Jones potential incorporating the main contribution of the three-body interactions. To this end, the ratio of three-body to two-body configuration energies have been determined also from Monte Carlo simulation. The results for the pressure and energy at supercritical temperatures are in quite good agreement with experimental data. The liquid–vapor coexistence is also reproduced fairly well, although for Ar and Kr the critical temperature is slightly overestimated as well as the liquid densities at low temperatures, and the coexistence densities of Xe are slightly overestimated for the vapor and underestimated for the liquid near the critical point. In any case, the calculations show a remarkable improvement in the predicted coexistence curve with including the three-body contribution.

Polarization effects in the total rate of biharmonic ω+3ω ionization of atoms

The total ionization rate of biharmonic ($\ensuremath{\omega}+3\ensuremath{\omega}$) ionization is studied within the independent particle approximation and the third-order perturbation theory. Particular attention is paid to how the polarization of the biharmonic light field affects the total rate. The ratios of the biharmonic ionization rates for linearly and circularly polarized beams as well as for corotating and counter-rotating elliptically polarized beams are analyzed, and how they depend on the beam parameters, such as photon frequency or phase between $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ light beams. We show that the interference of the biharmonic ionization amplitudes determines the dominance of a particular beam polarization over another and that it can be controlled by an appropriate choice of beam parameters. Furthermore, we demonstrate our findings for the ionization of neon $L$ shell electrons.

Benchmarking CASPT3 vertical excitation energies.

Based on 280 reference vertical transition energies of various excited states (singlet, triplet, valence, Rydberg, n → π*, π → π*, and double excitations) extracted from the QUEST database, we assess the accuracy of complete-active-space third-order perturbation theory (CASPT3), in the context of molecular excited states. When one applies the disputable ionization-potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11eV. However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespective of the transition type and system size, with a small reduction in the mean absolute error to 0.09eV when the IPEA shift is switched off.

On the choice of the effective diameter in the high-temperature expansion for the Lennard–Jones fluid

A third-order perturbation theory, within the framework of the high temperature expansion, with the perturbation terms obtained from computer simulation, is used to test the performance of several prescriptions proposed in the literature to obtain the effective hard-sphere diameter for the Lennard–Jones fluid. It is found that the classical Barker–Henderson prescription provides, on the whole, the best accuracy as compared with the available simulation data for the excess energy, the equation of state and the liquid-vapour coexistence densities.

Using the first-order, second-order, and third-order interpolation perturbation theory from quantum mechanics of modern physics to predict the CGM sensor device’s fasting plasma glucose value in the early morning, while analyzing their associated waveform shape similarities over a 14-month period based on GH-Method: math-physical medicine (No. 561)

The author utilizes the first-order, second-order, and third-order interpolation perturbation equations from quantum mechanics of modern physics to his medical research work, which he has previously written a few medical articles on this topic. This equation is the simplest application using one selected “perturbation factor” to generate perturbed results with high prediction accuracy and waveform shape similarity. During November 2021, he has applied the statistics regression analysis model to analyze the relationship among many biomarkers where he wrote ~20 medical articles. In this study, he predicts his fasting plasma glucose (FPG) value from his body temperature (BT) and body weight (BW) in the early morning. As a comparison, he chose two separate perturbation values of 0.4 for BT perturbation factor and 0.6 for BW perturbation factor to calculate and predict his FPG value. He then compares the predicted FPG dataset against his measured sensor FPG dataset. This comparison study also contains the following two final measurement yardsticks to confirm the usefulness of the perturbed method. The first yardstick is to verify the prediction accuracies of the perturbed FPG dataset against his measured FPG dataset. The second yardstick is to examine the waveform shape similarity via the calculated correlation coefficient between the predicted or perturbed, FPG curve and the measured FPG curve. In summary, the purpose of this study is to investigate the prediction accuracy and the waveform shape similarities between a perturbed or predicted FPG waveform and his measured FPG waveform over a 14-month period, which is a total of 420 days from 10/1/2020 to 11/24/2021. He utilizes the first-order, second-order, and third-order of interpolation perturbation equations with two different perturbation factor values of 0.4 for BT and 0.6 for BW. The author has selected these two slightly different slopes, i.e., perturbation values, to study the sensitivity results. The two conclusions drawn from this research work are listed as follows: First, the 3 perturbation equations for the BT and BW cases offered an identical match for waveform shape similarity with a 100% correlation coefficient. Second, the 3 perturbation equations also provided extremely high prediction accuracies as outlined: Prediction Accuracy for BT Case (Perturbation Value 0.4) First-order: Accuracy = 96% Second-order: Accuracy = 95% Third-order: Accuracy = 94%Prediction Accuracy for BW case (Perturbation Value 0.6) First-order: Accuracy = 98% Second-order: Accuracy = 96% Third-order: Accuracy = 95% All 6 prediction accuracies are higher than 94%. It seems that the higher the slope (perturbation value), the higher prediction accuracy will be achieved.

The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules.

We use the GW100 benchmark set to systematically judge the quality of several perturbation theories against high-level quantum chemistry methods. First of all, we revisit the reference CCSD(T) ionization potentials for this popular benchmark set and establish a revised set of CCSD(T) results. Then, for all of these 100 molecules, we calculate the HOMO energy within second and third-order perturbation theory (PT2 and PT3), and, GW as post-Hartree-Fock methods. We found GW to be the most accurate of these three approximations for the ionization potential, by far. Going beyond GW by adding more diagrams is a tedious and dangerous activity: We tried to complement GW with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (W TDHF), and with a GW density-matrix (γ GW ). Only the γ GW result has a positive impact. Finally using an improved hybrid functional for the non-interacting Green’s function, considering it as a cheap way to approximate self-consistency, the accuracy of the simplest GW approximation improves even more. We conclude that GW is a miracle: Its subtle balance makes GW both accurate and fast.

Multicomponent MP4 and the inclusion of triple excitations in multicomponent many-body methods.

This study implements the full multicomponent third-order (MP3) and fourth-order (MP4) many-body perturbation theory methods for the first time. Previous multicomponent studies have only implemented a subset of the full contributions, and the present implementation is the first multicomponent many-body method to include any connected triples contribution to the electron-proton correlation energy. The multicomponent MP3 method is shown to be comparable in accuracy to the multicomponent coupled-cluster doubles method for the calculation of proton affinities, while the multicomponent MP4 method is of similar accuracy as the multicomponent coupled-cluster singles and doubles method. From the results in this study, it is hypothesized that the relative accuracy of multicomponent methods is more similar to their single-component counterparts than previously assumed. It is demonstrated that for multicomponent MP4, the fourth-order triple-excitation contributions can be split into electron-electron and electron-proton contributions and the electron-electron contributions ignored with very little loss of accuracy of protonic properties.

Nonperturbative quasiclassical theory of graphene photoconductivity

We present a nonperturbative quasi-classical theory of graphene photoconductivity. We consider the influence of low-frequency (microwave, terahertz, mid-infrared) radiation on the static conductivity of a uniform graphene layer and calculate its photoconductivity as a function of frequency, polarization and strength of the external ac electric field, as well as on the material properties (electron density, scattering time) and temperature. The theory is valid at frequencies $\hbar\omega\lesssim 2E_F$ and at arbitrarily strong ac electric fields. We compare our results with those of the third-order perturbation theory and determine the applicability range of the perturbative solutions.

A complex absorbing potential electron propagator approach to resonance states of metastable anions

An earlier developed electron propagator method for the treatment of electron attachment to molecules within the non-Dyson algebraic-diagrammatic construction framework (EA-ADC) is extended by inclusion of the complex absorbing potential (CAP). The resulting method allows for the investigation of resonance states of metastable anions. Approximation schemes up to third-order perturbation theory for the electron propagator (EA-ADC(3)) are implemented. The CAP operator is treated up to second-order using the intermediate state representation formalism (ISR(2)) and the subspace projection technique. The CAP/EA-ADC(3) method is tested in first applications to the resonances in CO and N2 molecules associated with electron attachment to their low-lying π*-orbitals. The results of the calculations agree well with the available experimental and theoretical data and demonstrate the CAP-augmented EA-ADC modeling can become a useful tool for theoretical studies of metastable electron-attached states.

Application of Higher-Order Interpolation Perturbation Theory on Postprandial Plasma Glucose Waveform of a Single Lunch Based on GH-Method: Math-Physical Medicine (No. 426)

In this particular research note, the author arbitrarily selects the postprandial plasma glucose (PPG) data and waveforms from his lunch on 3/31/21 as the reference base. He then applies the higher-order, including first-order, second-order, and third-order interpolation perturbation theory to generate three approximated PPG waveforms to compare them against the measured nonlinear PPG waveform. The two major purposes of this study is to check the waveform shape similarity via correlation coefficients and the prediction accuracy via comparison of the averaged PPG values using the “higher order” interpolation perturbation theory. One obvious conclusion can be drawn from this article is that the higher-order perturbation equation provides a better approximate solution. However, in reality, there are very few patients who understand the perturbation theory of quantum mechanics, let alone to be able to conduct the complex mathematical calculations in order to achieve their desired glucose projection.

Accurate initial conditions for cosmological N-body simulations: minimizing truncation and discreteness errors

ABSTRACT Inaccuracies in the initial conditions for cosmological N-body simulations could easily be the largest source of systematic error in predicting the non-linear large-scale structure. From the theory side, initial conditions are usually provided by using low-order truncations of the displacement field from Lagrangian perturbation theory, with the first- and second-order approximations being the most common ones. Here, we investigate the improvement brought by using initial conditions based on third-order Lagrangian perturbation theory (3LPT). We show that with 3LPT, truncation errors are vastly suppressed, thereby opening the portal to initializing simulations accurately as late as z = 12 (for the resolution we consider). We analyse the competing effects of perturbative truncation and particle discreteness on various summary statistics. Discreteness errors are essentially decaying modes and thus get strongly amplified for earlier initialization times. We show that late starting times with 3LPT provide the most accurate configuration, which we find to coincide with the continuum fluid limit within 1 per cent for the power- and bispectrum at z = 0 up to the particle Nyquist wavenumber of our simulations (k ∼ 3h Mpc−1). In conclusion, to suppress non-fluid artefacts, we recommend initializing simulations as late as possible with 3LPT. We make our 3LPT initial condition generator publicly available.