Polarization Contribution Research Articles

Calculating Vertical Ionization Energies of Hydrated Biological Chromophores Based on Multiconfigurational Perturbation Theory

Here we introduce a methodology for calculating vertical detachment energies (VDE) and vertical ionization energies (VIE) of anionic and neutral chromophores in aqueous environment. The proposed method is based on the extended multiconfigurational quasidegenerate perturbation theory coupled to the explicit treatment of solvent effects in the frame of the effective fragment potential method. We show that the solvent polarization contribution must be considered for getting accurate quantitative estimations of VDEs and VIEs. The calculated values of VDE for phenolate (7.3 eV) and VIE for phenol (7.9 eV) in aqueous environment are in good agreement with the experimental results obtained using X-ray and multiphoton UV photoelectron spectroscopy. Our approach will be useful for studying processes of photoinduced electron transfer from anionic as well as neutral biological chromophores in aqueous solution.

Calculating Vertical Ionization Energies of Hydrated Biological Chromophores Based on Multiconfigurational Perturbation Theory

Here we introduce a methodology for calculating vertical detachment energies (VDE) and vertical ionization energies (VIE) of anionic and neutral chromophores in aqueous environment. The proposed method is based on the extended multiconfigurational quasidegenerate perturbation theory coupled to the explicit treatment of solvent effects in the frame of the effective fragment potential method. We show that the solvent polarization contribution must be considered for getting accurate quantitative estimations of VDEs and VIEs. The calculated values of VDE for phenolate (7.3 eV) and VIE for phenol (7.9 eV) in aqueous environment are in good agreement with the experimental results obtained using X-ray and multiphoton UV photoelectron spectroscopy. Our approach will be useful for studying processes of photoinduced electron transfer from anionic as well as neutral biological chromophores in aqueous solution.

Coordinate-space calculation of the window observable for the hadronic vacuum polarization contribution to (g−2)μ

The `intermediate window quantity' of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon allows for a high-precision comparison between the data-driven approach and lattice QCD. The existing lattice results, which presently show good consistency among each other, are in strong tension with the data-driven determination. In order to check for a potentially common source of systematic error of the lattice calculations, which are all based on the time-momentum representation (TMR), we perform a calculation using a Lorentz-covariant coordinate-space (CCS) representation. We present results for the isovector and the connected strange-quark contributions to the intermediate window quantity at a reference point in the $(m_\pi,m_K)$ plane, in the continuum and infinite-volume limit, based on four different lattice spacings. Our results are in good agreement with those of the recent TMR-based Mainz-CLS publication.

An Improved Core-Corona Model for Λ and Λ Polarization in Relativistic Heavy-Ion Collisions

Due to its sensitivity to the dynamics of strongly interacting matter subject to extreme conditions, hyperon global polarization has become an important observable to study the system created in relativistic heavy-ion collisions. Recently, the STAR and HADES collaborations have measured the global polarization of both Λ and Λ¯ produced in semi-central collisions in a wide range of collision energies. The polarization excitation functions show an increasing trend as the collision energy decreases, with the increase being more pronounced for the Λ¯. In this work, we make a summary of a core-corona model that we have developed to quantify the global polarization contributions from Λ and Λ¯ created in different regions of the fireball. The core-corona model assumes that Λs and Λ¯s are produced in both regions, the high-density core and the lower density corona, with different relative abundances which modulate the polarization excitation function. We have shown that the model works well for the description of experimental results. The global polarization excitation functions computed with the model show a peak at different collision energies in the region sNN≤10 GeV. Finally, we discuss and report on the model global polarization predictions for BES-II, NICA and CBM at FAIR and HADES energies.

Muon g-2 with overlap valence fermions

We present a lattice calculation of the leading order (LO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment for the connected light and strange quarks, $a^{\rm W}_{{\rm con}, l/s}$ in the widely used window $t_0=0.4~\mathrm{fm}$, $t_1=1.0~\mathrm{fm}$, $\Delta=0.15~\mathrm{fm}$, and also of $a^{\rm S}_{{\rm con}, l/s}$ in the short distance region. We use overlap fermions on 4 physical-point ensembles. Two 2+1 flavor RBC/UKQCD ensembles use domain wall fermions (DWF) and Iwasaki gauge actions at $a = 0.084$ and 0.114 fm, and two 2+1+1 flavor MILC ensembles use the highly improved staggered quark (HISQ) and Symanzik gauge actions at $a = 0.088$ and 0.121 fm. We have incorporated infinite volume corrections from 3 additional DWF ensembles at ${\rm L}$ = 4.8, 6.4 and 9.6 fm and physical pion mass. For $a^{\rm W}_{{\rm con}, l}$, we find that our results on the two smaller lattice spacings are consistent with those using the unitary setup, but those at the two coarser lattice spacings are slightly different. Eventually, we predict $a^{\rm W}_{{\rm con}, l}=206.7(1.5)(1.0)$ and $a^{\rm W}_{{\rm con}, s}=26.8(0.1)(0.3)$, using linear extrapolation in $a^2$, with systematic uncertainties estimated from the difference of the central values from the RBC/UKQCD and MILC ensembles.

Measurements of electron bremsstrahlung double-differential cross sections for solid targets down to low photon energies: No polarization contribution

The authors measured the bremsstrahlung double-differential cross sections for some solid thin-film elemental targets by kilovolt electron impact down to low photon energies. The results definitely show that there is no polarization bremsstrahlung contribution in solid-target experiments.

Electron collision with Ammonia and phosphine at wide range of energies

The NH3 and PH3 molecules achieve differential electron elastic scattering cross-sections for energies ranging from 15 eV to 500 eV for ammonia and from 5 to 500 eV for phosphine. Calculations are performed using partial waveforms describing the target molecule using a single Hartree-Fock Molecular Function Center. The potentials used include a constant part—numerically obtained from quantum computation in addition to subtle effects such as correlation, polarization, and potential exchange, results of this model clearly show the role of the exchange, as well as the contributions of correlation and polarization, especially at low scattering angles and incident energies. The differential cross-sections obtained were compared with a large amount of experimental data from the research, and good agreement was found. Throughout the scattering angles and power ranges examined here. http://dx.doi.org/10.31257/2018/JKP/2022/140208

Characterisation of the Surface Free Energy of the Recycled Cellulose Layer that Comprises the Middle Component of Corrugated Paperboards

The objective of this study was to determine the polar and dispersive surface free-energy (SFE) components of the central layer of corrugated paperboards, which are made of recycled fibres. The polar and dispersive components of, and the total, SFE (also known as interfacial energy) were calculated from the contact angles of water and diiodomethane liquids on recycled cellulose sheets. The total SFE of the middle component layers of two different grammages which comprised recycled fibres ranged from 47.9 mN/m to 51.05 mN/m. The contribution of the polar component to the total surface free energy of the two types of sheets ranged from 8.6 mN/m to 12.6 mN/m. This polar contribution was significantly lower than that of water. The contact angle method proved to be a consistent way to estimate the surface properties of industrially made recycled paper products.

Pulsar polarization: a broad-band population view with the Parkes Ultra-Wideband receiver

ABSTRACTThe radio polarization properties of the pulsar population are only superficially captured by the conventional picture of pulsar radio emission. We study the broadband polarization of 271 young radio pulsars, focusing particularly on circular polarization, using high-quality observations made with the Ultra-Wideband Low receiver on Murriyang, the Parkes radio telescope. We seek to encapsulate polarization behaviour on a population scale by defining broad categories for frequency- and phase-dependent polarization evolution, studying the co-occurrences of these categorizations and comparing them with average polarization measurements and spin-down energy ($\dot{E}$). This work shows that deviations of the linear polarization position angle from the rotating vector model are linked to the presence of circular polarization features and to frequency evolution of the polarization. Polarization fraction, circular polarization contribution, and profile complexity all evolve with $\dot{E}$ across the population, with the profiles of high-$\dot{E}$ pulsars being simple and highly linearly polarized. The relationship between polarization fraction and circular contribution is also seen to evolve such that highly polarized profiles show less variation in circular contribution with frequency than less strongly polarized profiles. This evolution is seen both across the population and across frequency for individual sources. Understanding pulsar radio polarization requires detailed study of individual sources and collective understanding of population-level trends. For the former, we provide visualizations of their phase- and frequency-resolved polarization parameters. For the latter, we have highlighted the importance of including the impact of circular polarization and of $\dot{E}$.

Origin of Ferromagnetic Exchange Coupling in Donor–Acceptor Biradical Analogues of Charge-Separated Excited States

A new donor-acceptor biradical complex, TpCum,MeZn(SQ-VD) (TpCum,MeZn+ = zinc(II) hydro-tris(3-cumenyl-5-methylpyrazolyl)borate complex cation; SQ = orthosemiquinone; VD = oxoverdazyl), which is a ground-state analogue of a charge-separated excited state, has been synthesized and structurally characterized. The magnetic exchange interaction between the S = 1/2 SQ and the S = 1/2 VD within the SQ-VD biradical ligand is observed to be ferromagnetic, with JSQ-VD = +77 cm-1 (H = -2JSQ-VDŜSQ·ŜVD) determined from an analysis of the variable-temperature magnetic susceptibility data. The pairwise biradical exchange interaction in TpCum,MeZn(SQ-VD) can be compared with that of the related donor-acceptor biradical complex TpCum,MeZn(SQ-NN) (NN = nitronyl nitroxide, S = 1/2), where JSQ-NN ≅ +550 cm-1. This represents a dramatic reduction in the biradical exchange by a factor of ∼7, despite the isolobal nature of the VD and NN acceptor radical SOMOs. Computations assessing the magnitude of the exchange were performed using a broken-symmetry density functional theory (DFT) approach. These computations are in good agreement with those computed at the CASSCF NEVPT2 level, which also reveals an S = 1 triplet ground state as observed in the magnetic susceptibility measurements. A combination of electronic absorption spectroscopy and CASSCF computations has been used to elucidate the electronic origin of the large difference in the magnitude of the biradical exchange coupling between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN). A Valence Bond Configuration Interaction (VBCI) model was previously employed to highlight the importance of mixing an SQSOMO → NNLUMO charge transfer configuration into the electronic ground state to facilitate the stabilization of the high-spin triplet (S = 1) ground state in TpCum,MeZn(SQ-NN). Here, CASSCF computations confirm the importance of mixing the pendant radical (e.g., VD, NN) LUMO (VDLUMO and NNLUMO) with the SOMO of the SQ radical (SQSOMO) for stabilizing the triplet, in addition to spin polarization and charge transfer contributions to the exchange. An important electronic structure difference between TpCum,MeZn(SQ-VD) and TpCum,MeZn(SQ-NN), which leads to their different exchange couplings, is the reduced admixture of excited states that promote ferromagnetic exchange into the TpCum,MeZn(SQ-VD) ground state, and the intrinsically weaker mixing between the VDLUMO and the SQSOMO compared to that observed for TpCum,MeZn(SQ-NN), where this orbital mixing is significant. The results of this comparative study contribute to a greater understanding of biradical exchange interactions, which are important to our understanding of excited-state singlet-triplet energy gaps, electron delocalization, and the generation of electron spin polarization in both the ground and excited states of (bpy)Pt(CAT-radical) complexes.

Locality in amino-acid based imidazolium ionic liquids.

Several amino-acid based imidazolium ILs are investigated through the use of ab initio molecular dynamics (AIMD), which includes full polarization. The electric dipole moment distribution and polarization is used as a means of characterizing and understanding these complex systems. Various charge scheme methods were analyzed (Wannier function, Blöchl, Löwdin and Mulliken charge schemes and Voronoi tessellation) to determine their ability to predict dipole moments. These results and the following comparison of methods further deepen the knowledge of polarization by highlighting the importance of the anion and cation separately on polarizability contribution and the need to select a suitable method to predict these. The angular probability distribution is utilized to measure the degree of locality in monopole-dipole electrostatic interactions, which showed no preferential alignment over 700 pm. In addition, the IR and Raman spectra from Voronoi tessellation of [C2C1Im][ala] were analyzed. In these, the strongest signalling peaks showed consistency with experiment and the ability to differentiate between anion and cation components of the IL.

Influence of magnetic field on the dielectric characteristics in manganese sulfide substituted with thulium

The properties of a solid solution of thulium-substituted manganese sulfide prepared by melting the initial pure samples of manganese sulfide and thulium sulfide are studied. X-ray diffraction analysis was carried out. The face-centered cubic lattice is determined, and the decrease in the intensity of the peaks is found. Dielectric permittivity was measured in the frequency range 102106 Hz and temperatures 300-500 K in magnetic fields up to 12 kOe in TmxMn1xS solid solutions (0 x 0,15). From the frequency dependence of the permittivity, the relaxation time and the relaxation mechanism of the dipole moments are found. The leakage current is excluded, and the contribution of migration polarization due to charges in the region with chemical phase separation is estimated. Die real and imaginary components of the permittivity of TmxMn1xS samples are described in the Debye model. The maximum of the imaginary component of the permittivity shifts towards higher frequencies upon heating, and the relaxation time is described by the Arrhenius function. Dielectric losses are caused by electron-phonon interaction. The frequency of the crossover from Debye relaxation to relaxation conduction associated with the absorption and emission of phonons is found. Die crossover frequency increases as the sample is heated according to a power law. In a magnetic field, the permittivity decreases and the largest change of 2.5 % is achieved at T = 450 K. At other temperatures, the magnetocapacitance does not exceed 0.5 %. The shift of the maximum of the imaginary component of the permittivity to low frequencies in a magnetic field leads to a change in the sign of dielectric losses from positive to negative. A qualitative difference in () is established in the vicinity of the concentration of thulium ion flow through the FCC lattice, where the permittivity is not described in the Debye model and there is no magnetocapacitance. The mechanism for reducing dielectric losses in a magnetic field is determined.

Leading hadronic contribution to the muon g − 2 from lattice QCD

We compute the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. The calculations are performed using four flavors of stout smeared staggered quarks, with quark masses at their physical values. The continuum limit is taken using six different lattice spacings ranging from 0.132 fm down to 0.064 fm. All strong isospin breaking and electromagnetic effects are accounted for to leading order. A controlled infinite volume limit is taken thanks to dedicated simulations performed in box sizes up to 11 fm. Putting all these ingredients together, we find [(gµ − 2)/2]LO−HVP = 707.5[5.5] 10−10, which has a total uncertainty of 0.8%. Compared to determinations based on the e+e− → hadrons cross section, our result significantly reduces the tension between the standard model prediction for the muon g − 2 and its experimental value.

Spectral Induced Polarization (SIP) of Denitrification‐Driven Microbial Activity in Column Experiments Packed With Calcareous Aquifer Sediments

AbstractSpectral Induced Polarization (SIP) has been suggested as a non‐invasive monitoring proxy for microbial processes. Under natural conditions, however, multiple and often coupled polarization processes co‐occur, impeding the interpretation of SIP signals. In this study, we analyze the sensitivity of SIP to microbially‐driven reactions under quasi‐natural conditions. We conducted flow‐through experiments in columns equipped with SIP electrodes and filled with natural calcareous, organic‐carbon‐rich aquifer sediment, in which heterotrophic denitrification was bio‐stimulated. Our results show that, even in the presence of parallel polarization processes in a natural sediment under field‐relevant geochemical conditions, SIP is sufficiently sensitive to microbially‐driven changes in electrical charge storage. Denitrification yielded an increase in imaginary conductivity of up to 3.1 (+140%) and the formation of a distinct peak between 1 and 10 Hz, that matched the timing of expected microbial activity predicted by a reactive transport model fitted to solute concentrations. A Cole‐Cole decomposition allowed separating the polarization contribution of microbial activity from that of cation exchange, thereby helping to locate microbial hotspots without the need for (bio)geochemical data to constrain the Cole‐Cole parameters. Our approach opens new avenues for the application of SIP as a rapid method to monitor a system's reactivity in situ. While in preceding studies the SIP signals of microbial activity in natural sediments were influenced by mineral precipitation/dissolution reactions, the imaginary conductivity changes measured in the biostimulation experiments presented here were dominated by changes in the polarization of the bacterial cells rather than a reaction‐induced alteration of the abiotic matrix.

Rationalization of supramolecular interactions of a newly synthesized binuclear Cu(II) complex derived from 4,4′,6,6′-tetramethyl 2,2′-bipyrimidine ligand through Hirshfeld surface analysis

A new binuclear copper (II) complex [Cu2L2Cl4(H2O)2] (1) derived from 4,4',6,6'-tetramethyl-2,2'-bipyrimidine (L) has been synthesized and characterized by the single crystal X-ray diffraction method. Single crystal analysis of complex 1 reveals that it crystallizes in the space group P21/n under a monoclinic system (β = 97.995(2)°, a = 7.6483(2), b = 7.2158(3) and c = 17.8477(6) Å). The ligand acts as a bis-bidentate one and each copper (II) center bears a square pyramidal geometry exploiting N2Cl2O chromophore. In the solid state, the complex is stabilized through classical O-H···Cl intermolecular hydrogen bonding incorporating coordinated water (as a solvent) and chloride ions and lone pair···π interactions. The Hirshfeld surface analysis demonstrates H···H/H···H, H···Cl/Cl···H, H···C/C···H, and C···Cl/Cl···C intermolecular interactions as the major contributor interactions in the solid-state packing of the molecular crystal. Interaction energy calculations carried out employing the wavefunction generated via B3LYP/6-31G(d,p) highlight the dominance of electrostatic energy and the contribution of polarization and dispersion energy towards the total energy of complex 1 in the solid state.

MUonE, muon g−2 and electroweak precision constraints within 2HDMs

Two Higgs doublet models are attractive scenarios for physics beyond the Standard Model. In particular, lepton-specific manifestations remain contenders to explain the observed discrepancy between the anomalous magnetic moment of the muon $a_\mu$ predicted within the Standard Model and recent observations at Fermilab and BNL. Dominant uncertainties that affect $a_\mu$ have motivated the MUonE experiment to access the hadronic vacuum polarisation contribution that impacts $a_\mu$ via elastic muon-electron scattering. In this work, we contrast the high precision that is achievable within the MUonE context with constraints from flavour physics, precision electroweak constraints and LHC searches as well as their extrapolations for a range of two Higgs doublet models with a softly broken $\mathbb{Z}_2$ symmetry. We find that the sensitivity of MUonE does not extend beyond the parameter regions that are already excluded by other constraints. MUonE will therefore provide a detailed measurement of the hadronic vacuum polarisation contribution which then transparently informs $a_\mu$ interpretations in 2HDMs without modifications of correlations from beyond the Standard Model interactions. In passing we extend earlier results of LHC and flavour projections to lepton-specific 2HDM (Types X and Y) scenarios, and comment on the possibility of modifying the value of the W-boson mass; we briefly discuss the implications for a strong first-order electroweak phase transition for these models.

Involvement of the -C(O)-CH=CH- linker chain in different π interactions in crystalline chalcones, (2E)-phenyl-C(=O)-CH=CH-benzene derivatives. Importance of anti-parallel layered motifs in benzyloxy substituted compounds

X-ray crystallographic, Hirshfeld surface and PIXEL study is reported on five benzyloxy substituted compounds, namely (E)-3-[2 methoxy‑5-benzyloxyphenyl]-1-(2‑hydroxy-4-methoxyphenyl)-2-ene-1-one, compound 1, (E)-3-[2,5-bis(benzyloxy)phenyl]-1-(2-hydroxyphenyl)-2-ene-1-one, compound 2, (E)-3-[2,5-bis(benzyloxy)phenyl]-1-(2‑hydroxy-4-methoxyphenyl)-2-ene-1-one, compound 3, (E)-3-[2,5-bis(benzyloxy)phenyl]-1-(2‑hydroxy-3,4-dimethoxyphenyl)-2-ene-1-one, compound 4, and (E)-3-[2,5-bis(benzyloxy)phenyl]-1-(2‑hydroxy-4,5-dimethoxyphenyl)-2-ene-1-one, compound 5. All five compounds exhibit intramolecular O—H(hydroxyl)···O(carbonyl) classical hydrogen bonds, (E)-arrangements about the olefinic bond and near planar chalcone cores, with the interplanar angles between chalcone rings A and B all less than 10°. The phenyl groups in the benzyloxy substituents make much greater interplanar angles with the chalcone core rings, A and B. The linker units, -C(O)-CH=CH-, between the terminal phenyl rings in the chalcone cores, exhibit electronic delocalization as indicated by the bond lengths being between single and double bonds. Motifs having molecules aligned in antiparallel arrangements in layers, with perpendicular distances between the two layers of ca.3.5 Å are amongst the most important motifs. The molecular slippage of the antiparallel molecules in these motifs varies significantly, which results in different functionality, e.g., the terminal phenyl rings, or segments in the linker unit, such as the carbonyl or the olefinic groups, in one layer being suitably placed to interact with functionality in the other. This series of motifs illustrate a great range of slippage distances which is reflected in the variety of interactions present in the motifs, including off-set, face-to-face π···π, π(CO)···π, π(CO)···π(CO) and π(C=C)···π(C=C) interactions. PIXEL calculations reveal the important motifs and their energies, and generally indicate the much greater importance of the dispersive contribution than Coulombic and polarization contributions to the overall energies of these molecules.

Abstracts

In this article, the effect of Zr addition on the crystalline structure, ferroelectric and piezoelectric properties of Barium Strontium Titanate (BST) ceramic have been studied. Zr was doped in the range of 0 ≤ x ≤ 0.20 in Ba0.90Sr0.10Ti1-xZrxO3 (BSZT) and it was prepared via solid state reaction technique. From the characterization studies, it was realized that Zr addition in BSZT ceramics results in slight modification of BSZT lattice, but due to diffusion of Zr into the lattice, the crystallite size as well as the microstructure of combined BSZT system got modified drastically. Zr addition in BSZT ceramics results in increase of lattice parameter due to larger ionic radius of Zr ions compared to Ti ions. Reduction of grain and crystallite size was also observed, which affects the ferroelectric behaviour of BSZT ceramic by influencing the polarization contribution from individual domains. This causes a slow transformation of sharp paraelectric-ferroelectric transition to diffusive ferroelectric phase transition and it also introduces relaxation phenomenon in the system at higher Zr compostion, which convert it to a relaxor ferroelectric. At relaxor phase a decreased spontaneous polarization and slimmer P–E hysteresis loop was observed with increasing Zr content. The main reason behind this conversion and modification in microstructural properties is because of the presence of strain in BSZT lattice which is due to replacement of Zr4+ (0.72 Å) inplace of smaller Ti4+ (0.609 Å) in more than a tolerable limit. Substitution of Zr4+ for Ti4+ in BaSrTiO3 introduces structural disorder, causing perturbations like local electric and strain fields. These perturbations reduce the long-range polar order resulting in relaxor behavior.

Effect of Zr substitution on electrical properties of Ba0.90Sr0.10Ti1−xZrxO3 (0 ≤ x ≤ 0.20) ceramics

In this article, the effect of Zr addition on the crystalline structure, ferroelectric and piezoelectric properties of Barium Strontium Titanate (BST) ceramic have been studied. Zr was doped in the range of 0 ≤ x ≤ 0.20 in Ba0.90Sr0.10Ti1-xZrxO3 (BSZT) and it was prepared via solid state reaction technique. From the characterization studies, it was realized that Zr addition in BSZT ceramics results in slight modification of BSZT lattice, but due to diffusion of Zr into the lattice, the crystallite size as well as the microstructure of combined BSZT system got modified drastically. Zr addition in BSZT ceramics results in increase of lattice parameter due to larger ionic radius of Zr ions compared to Ti ions. Reduction of grain and crystallite size was also observed, which affects the ferroelectric behaviour of BSZT ceramic by influencing the polarization contribution from individual domains. This causes a slow transformation of sharp paraelectric-ferroelectric transition to diffusive ferroelectric phase transition and it also introduces relaxation phenomenon in the system at higher Zr compostion, which convert it to a relaxor ferroelectric. At relaxor phase a decreased spontaneous polarization and slimmer P–E hysteresis loop was observed with increasing Zr content. The main reason behind this conversion and modification in microstructural properties is because of the presence of strain in BSZT lattice which is due to replacement of Zr4+ (0.72 Å) inplace of smaller Ti4+ (0.609 Å) in more than a tolerable limit. Substitution of Zr4+ for Ti4+ in BaSrTiO3 introduces structural disorder, causing perturbations like local electric and strain fields. These perturbations reduce the long-range polar order resulting in relaxor behavior.

Addendum: Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (2022 J. Phys. G: Nucl. Part. Phys. 49 055001)

This addendum provides results complementary to those obtained in [J. Phys. G 49, 055001 (2022)]. Specifically, an equivalent form of the relation, which binds together the ‘spacelike’ kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment , is obtained. It is shown that the infrared limiting value of the ‘spacelike’ and ‘timelike’ kernel functions, which enter the representations for involving the Adler function and the R-ratio, is identical to the corresponding QED contribution to the muon anomalous magnetic moment of the preceding order in the electromagnetic coupling. The next-to-leading order contributions (which includes the leptonic and hadronic insertions) and (which includes the double hadronic insertion), are studied. The three kernel functions appearing in the representations for , which involve the hadronic vacuum polarization function, Adler function, and the R-ratio, are presented for the cases of the electron and τ-lepton loop insertions.