Perturbative Corrections Research Articles

Generalized perturbative singles corrections to the random phase approximation method: Impact on noncovalent interaction energies of closed- and open-shell dimers.

The post-Kohn-Sham (KS) random phase approximation (RPA) method may provide a poor description of interaction energies of weakly bonded molecules due to inherent density errors in approximate KS functionals. To overcome these errors, we develop a generalized formalism to incorporate perturbative singles (pS) corrections to the RPA method using orbital rotations as a perturbation parameter. The pS schemes differ in the choice of orbital-rotation gradient and Hessian. We propose a pS scheme termed RPA singles (RPAS)[Hartree-Fock (HF)] that uses the RPA orbital-rotation gradient and time-dependent HF Hessian. This correction reduces the errors in noncovalent interaction energies of closed- and open-shell dimers. For the open-shell dimers, the RPAS(HF) method leads to a consistent error reduction by 50% or more compared to the RPA method for the cases of hydrogen-bonding, metal-solvent, carbene-solvent, and dispersion interactions. We also find that the pS corrections are more important in error reduction compared to higher-order exchange corrections to the RPA method. Overall, for open shells, the RPAS(HF)-corrected RPA method provides chemical accuracy for noncovalent interactions and is more reliable than other perturbative schemes and dispersion-corrected density functional approximations, highlighting its importance as a reliable beyond-RPA correction.

Rapid Online Corrections for Proprioceptive and Visual Perturbations Recruit Similar Circuits in Primary Motor Cortex.

An important aspect of motor function is our ability to rapidly generate goal-directed corrections for disturbances to the limb or behavioral goal. The primary motor cortex (M1) is a key region involved in processing feedback for rapid motor corrections, yet we know little about how M1 circuits are recruited by different sources of sensory feedback to make rapid corrections. We trained two male monkeys (Macaca mulatta) to make goal-directed reaches and on random trials introduced different sensory errors by either jumping the visual location of the goal (goal jump), jumping the visual location of the hand (cursor jump), or applying a mechanical load to displace the hand (proprioceptive feedback). Sensory perturbations evoked a broad response in M1 with ∼73% of neurons (n = 257) responding to at least one of the sensory perturbations. Feedback responses were also similar as response ranges between the goal and cursor jumps were highly correlated (range of r = [0.91, 0.97]) as were the response ranges between the mechanical loads and the visual perturbations (range of r = [0.68, 0.86]). Lastly, we identified the neural subspace each perturbation response resided in and found a strong overlap between the two visual perturbations (range of overlap index, 0.73-0.89) and between the mechanical loads and visual perturbations (range of overlap index, 0.36-0.47) indicating each perturbation evoked similar structure of activity at the population level. Collectively, our results indicate rapid responses to errors from different sensory sources target similar overlapping circuits in M1.

Effect of exohedral functionalization on the magnetic properties in the dysprosium-containing endohedral fullerene DySc2N@C80(CF2).

We present a quantum-chemical study of the effect of exohedral functionalization with a CF2 group on the lowest electronic states and the zero-field splitting pattern in a potential single-molecule magnet (SMM) compound DySc2N@C80(CF2). Multiconfiguration perturbational methodology is applied to various spin states of the endohedral compound, comparing different active spaces and state-averaging schemes in order to check for the possible involvement of orbitals other than 4f-Dy in the nondynamical electronic correlation and to suggest the most appropriate computational parameters. Combining the spin-orbit coupling calculations with perturbational corrections, we demonstrate that the interactions within the endohedral cluster and with the fullerene cage exert only a small effect on the non-relativistic approximation to the electronic states of the Dy3+ ion, yet they are significant enough to alter the parameters of zero-field splitting depending on the orientation of the DySc2N cluster inside the fullerene cage.

Electronic properties and collision cross sections of AgOkHm± (k, m = 1-4) aerosol ionic clusters.

Experimental evidence shows that hydroxylated metal ions are often produced during cluster synthesis by atmospheric pressure spark ablation. In this work, we predict the ground state equilibrium structures of AgOkHm± clusters (k and m = 1-4), which are readily produced when spark ablating Ag, using the coupled cluster with singles and doubles (CCSD) method. The stabilization energy of these clusters is calculated with respect to the dissociation channel having the lowest energy, by accounting perturbative triples corrections to the CCSD method. The interatomic interactions in each of the systems have been investigated using the frontier molecular orbital (FMO), natural bond orbital (NBO) and quantum theory of atoms in molecules (QTAIM) methods. Many of the ground states of these ionic clusters are found to be stable, corroborating experimental observations. We find that clusters having singlet spin states are more stable in terms of dissociation than the clusters that have doublet or triplet spin states. Our calculations also indicate a strong affinity of the ionic and neutral Ag atom towards water and hydroxyl radicals or ions. Many 3-center, 4-electron (3c/4e) hyperbonds giving rise to more than one resonance structure are identified primarily for the anionic clusters. The QTAIM analysis shows that the O-H and O-Ag bonds in the clusters of both polarities are respectively covalent and ionic. The FMO analysis indicates that the anionic clusters are more reactive than the cationic ones. Using the cluster structures predicted by the CCSD method, we calculate the collision cross sections of the AgOkHm± family, with k and m ranging from 1 to 4, by the trajectory method. In turn, we predict the electrical mobilities of these clusters when suspended in helium at atmospheric pressure and compare them with experimental measurements.

NLO corrections to the deeply virtual meson production revisited: impact on the extraction of generalized parton distributions

We revisit the next-to-leading order (NLO) perturbative QCD corrections for the deeply virtual meson production (DVMP) process, exploring its phenomenology both in isolation and in a multichannel fit combined with deeply virtual Compton scattering (DVCS). Our approach involves the conformal partial wave (CPaW) formalism, which allows for the straightforward inclusion of higher-order contributions and evolutionary effects. Our findings indicate that a description of the longitudinal component of the vector meson DVMP cross-section at high energies is achievable only at NLO within the standard collinear approach. Furthermore, we demonstrate a simultaneous description of DIS, DVCS, and DVMP processes, providing insights into the proton structure described at NLO by unique universal generalized parton distribution (GPD) functions.

On the physical viability of black hole solutions in Einsteinian Cubic Gravity and its generalisations

In this note, we discuss the pathological nature of black holes in Einsteinian Cubic gravity and its extensions. We compute the equations for the odd perturbations and show how spherically symmetric solutions that asymptotically approach a maximally symmetric space (Minkowski, de Sitter or anti-de Sitter) are associated to having an asymptotically degenerate principal part of the equations. We use these results to argue that the encountered problems will be generic for any other cubic or higher-order with a reduced linear spectrum around maximally symmetric spaces except the well-known healthy case of f(R). We highlight that these pathologies are only alarming when the theory is regarded as a complete theory, but not when considered as a perturbative correction to GR (as in e.g. the effective field theory framework) since the low-energy physics remains safe from them. Our results thus cast doubts on possible resolutions of the singularities or non-perturbative effects on horizons based on these theories.

Formula omitted] and TQQ within QCD Laplace sum rules

We present a review of our results for the masses and couplings of the scalar fully heavy four-quarks and TQQq¯q¯′(JP=0±,1±) tetraquarks states from (inverse) QCD Laplace sum rule (LSR), their ratios R and double ratio of sum rules (DRSR) within stability criteria and including Factorized Next-to-Leading Order (FNLO) Perturbative (PT) corrections. As the Operator Product Expansion (OPE) usually converges for d⩽6−8, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to 〈G3〉. Our results for the 0++ fully heavy four-quark states may explain the LHCb broad structure around (6.2−6.7)GeV which can be due to ηc‾ηc,χc1‾χc1 and J/ψ‾J/ψ molecules or/and their analogue ScSc,AcAc and VcVc tetraquarks. The peak at (6.8−6.9)GeV can be identified to the χc0‾χc0 molecule or/and the PcPc tetraquark state. Then, combining R and DRSR we focus on the analysis of the four-quark nature of Tccq¯q¯′1± and 0± states. We show that combining R and DRSR can provide more precise results: MTcc1+=3886(6)MeV and MTcc0+=3883(3)MeV. In a similar way, one obtain the improved mass predictions: MTccs¯u¯1+=3931(7)MeV, MTccs¯u¯0+=3983(7)MeV and MTccs¯s¯0+=3993(11)MeV. From our estimates of the masses of the Pseudoscalar and Vector Tccq¯q¯′ states, we observe that the interpolating currents lead to two classes: Class H (Heavy) states with masses around 6GeV and Class L (Light) states around (3.8−4.4)GeV where the pseudoscalar (resp. all vector states) are below the D‾D0,D‾sDs0 (resp. D‾D1,D‾sDs1) open charm thresholds. Finally, we extend the whole study to the bottom sector and confront our results with the ones from different LSR predictions and some other approaches (lattice, potential models, ⋯) in the literature.

Accelerating Coupled-Cluster Calculations with GPUs: An Implementation of the Density-Fitted CCSD(T) Approach for Heterogeneous Computing Architectures Using OpenMP Directives.

An algorithm is presented for the coupled-cluster singles, doubles, and perturbative triples correction [CCSD(T)] method based on the density fitting or the resolution-of-the-identity (RI) approximation for performing calculations on heterogeneous computing platforms composed of multicore CPUs and graphics processing units (GPUs). The directive-based approach to GPU offloading offered by the OpenMP application programming interface has been employed to adapt the most compute-intensive terms in the RI-CCSD amplitude equations with computational costs scaling as , , and (where NO and NV denote the numbers of correlated occupied and virtual orbitals, respectively) and the perturbative triples correction to execute on GPU architectures. The pertinent tensor contractions are performed using an accelerated math library such as cuBLAS or hipBLAS. Optimal strategies are discussed for splitting large data arrays into tiles to fit them into the relatively small memory space of the GPUs, while also minimizing the low-bandwidth CPU-GPU data transfers. The performance of the hybrid CPU-GPU RI-CCSD(T) code is demonstrated on pre-exascale supercomputers composed of heterogeneous nodes equipped with NVIDIA Tesla V100 and A100 GPUs and on the world's first exascale supercomputer named "Frontier", the nodes of which consist of AMD MI250X GPUs. Speedups within the range 4-8× relative to the recently reported CPU-only algorithm are obtained for the GPU-offloaded terms in the RI-CCSD amplitude equations. Applications to polycyclic aromatic hydrocarbons containing 16-66 carbon atoms demonstrate that the acceleration of the hybrid CPU-GPU code for the perturbative triples correction relative to the CPU-only code increases with the molecule size, attaining a speedup of 5.7× for the largest circumovalene molecule (C66H20). The GPU-offloaded code enables the computation of the perturbative triples correction for the C60 molecule using the cc-pVDZ/aug-cc-pVTZ-RI basis sets in 7 min on Frontier when using 12,288 AMD GPUs with a parallel efficiency of 83.1%.

Perturbative soft photon theorems in de Sitter spacetime

We define a perturbative S-matrix in a local patch of de Sitter background in the limit when the curvature length scale (ℓ) is large and study the ‘soft’ behavior of the scalar QED amplitudes in de Sitter spacetime in generic dimensions. We obtain the leading and subleading perturbative corrections to flat space soft photon theorems in the large ℓ limit, and comment on the universality of these corrections. We compare our results with the electromagnetic memory tails obtained earlier in d = 4 using classical radiation analysis.

Radiative Effects in Low-Dimensional Effective Fermion Field Theory with Compactification

The introduction of branes immersed in the space-times of higher dimensions revealed itself to be a useful instrument for the study of high-dimensional models in quantum field theory. Moreover, low-dimensional quantum field theories represent an especially interesting class of models in physics due to their unique properties and renormalizability when interactions are treated perturbatively. The advantages of both approaches can be combined in a model for a low-dimensional brane immersed in the usual tetradimensional Minkowski space-time, the properties of which are relatively well known. This approach can be used for the study of systems like graphene and carbon nanotubes. In the present work, we present an effective model for nanotubes based on the Lagrangian obtained from a tight-binding model for graphene. The induced current, appearing azimuthally in the presence of a magnetic flux through the tube section (Aharonov–Bohm effect), will be derived. A reduced Lagragian for photons confined on the tube surface, obtained from the literature, is included in the last part of the work to threat perturbative corrections to the induced current.

Generalization of the Tensor Product Selected CI Method for Molecular Excited States.

In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited-state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons with respect to the extrapolated result (i.e., near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.

Pion valence-quark generalized parton distribution at physical pion mass

We present the first lattice-QCD x-dependent pion valence-quark generalized parton distribution (GPD) calculated directly at physical pion mass using the Large-Momentum Effective Theory (LaMET) with next-to-next-to-leading order perturbative matching correction. We use clover fermions for the valence action on 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, with lattice spacing a≈0.09 fm and box size L≈5.5 fm; the pion two-point measurements number up to O(106) with boost momentum 1.73 GeV. The pion valence distribution is renormalized in hybrid scheme with Wilson-line mass subtraction at large distances in coordinate space, followed by a procedure to match it to the MS‾ scheme. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken x and the transverse impact-parameter distributions. We take the integral of our GPD functions to generate leading moment so that we can make comparisons with past lattice-QCD and experimental determinations of the pion form factors and found consistent agreement among them. We predict the higher GPD moments and reveal x-dependent tomography of the pion for the first time using lattice QCD.

Monte Carlo-calculated beam quality and perturbation correction factors validated against experiments for Farmer and Markus type ionization chambers in therapeutic carbon-ion beams

Objective. In current dosimetry protocols, the estimated uncertainty of the measured absorbed dose to water D w in carbon-ion beams is approximately 3%. This large uncertainty is mainly contributed by the standard uncertainty of the beam quality correction factor k Q. In this study, the k Q values in four cylindrical chambers and two plane-parallel chambers were calculated using Monte Carlo (MC) simulations in the plateau region. The chamber-specific perturbation correction factor P of each chamber was also determined through MC simulations. Approach. k Q for each chamber was calculated using MC code Geant4. The simulated k Q ratios in subjected chambers and reference chambers were validated through comparisons against our measured values. In the measurements in Heavy-Ion Medical Accelerator in Chiba, k Q ratios were obtained from D w values of 60Co, 290- and 400 MeV u−1 carbon-ion beams that were measured with the subjected ionization chamber and the reference chamber. In the simulations, f Q (the product of the water-to-air stopping power ratio and P) was acquired from D w and the absorbed dose to air calculated in the sensitive volume of each chamber. k Q values were then calculated from the simulated f Q and the literature-extracted W air and compared with previous publications. Main results. The calculated k Q ratios in the subjected chambers to the reference chamber agreed well with the measured k Q ratios. The k Q uncertainty was reduced from the current recommendation of approximately 3% to 1.7%. The P values were close to unity in the cylindrical chambers and nearly 1% above unity in the plane-parallel chambers. Significance. The k Q values of carbon-ion beams were accurately calculated in MC simulations and the k Q ratios were validated through ionization chamber measurements. The results indicate a need for updating the current recommendations, which assume a constant P of unity in carbon-ion beams, to recommendations that consider chamber-induced differences.

Excited-State-Specific Pseudoprojected Coupled-Cluster Theory.

We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional coupled-cluster wavefunction that allows correlation effects to be introduced atop an excited-state mean field starting point. The approach shares much in common with ground-state CCSD, including size extensivity and an N6 cost scaling. Preliminary numerical tests show that, when augmented with N5 cost perturbative corrections for key terms, the method can improve over excited-state-specific second-order perturbation theory in valence, charge transfer, and Rydberg states.

State-specific frozen natural orbital for reduced-cost algebraic diagrammatic construction calculations: The application to ionization problem.

We have developed a reduced-cost algebraic diagrammatic construction (ADC) method based on state-specific frozen natural orbital and natural auxiliary functions. The newly developed method has been benchmarked on the GW100 test set for the ionization problem. The use of state-specific natural orbitals drastically reduces the size of the virtual space with a systematically controllable accuracy and offers a significant speedup over the standard ionization potential (IP)-ADC(3) method. The accuracy of the method can be controlled by two thresholds and nearly a black box to use. The inclusion of the perturbative correction significantly improves the accuracy of the calculated IP values, and the efficiency of the method has been demonstrated by calculating the IP of a molecule with 60 atoms and more than 2216 basis functions.

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm.

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose-Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh-Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born-Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick's theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn-Luttinger-type nonconvergence.

Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants.

We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.

Scrutinizing the light scalar quarkonia from LSR at higher orders

We scrutinize, improve some determinations of the masses and couplings of light scalar quarkonia (q¯q and four-quark states) and present new results for the π+π−,K+K−,… molecules using QCD Laplace Sum Rule (LSR) truncated at the D=6 dimension vacuum condensates. We pay a special attention on the higher order perturbative (PT) corrections up to the (estimated) O(αs5) which improve the quality of the analysis. We request that the optimal results obey the rigorous constraint: Resonance ≥ QCD continuum contributions (RP/C≥1) in the LSR which excludes a Breit-Wigner/on-shell (not to be confused with a complex pole) scalar meson mass around (500-600) MeV obtained for values [tc≤(1∼1.5) GeV2] of the QCD continuum threshold. Mass-splittings due to SU(3) breakings are small. We discuss the different assignments of the observed scalar mesons below 2 GeV in the Conclusions where the I=0 states are compared with the scalar gluonia. The results are compiled in Tables 3 to 6. We hope that the systematic analysis done in this paper helps to clarify the complex spectra of the light scalar mesons.

Non-perturbative stabilization of two Kähler moduli in type-IIB/F theory and the inflaton potential

We consider a combination of perturbative and non-perturbative corrections in Kähler moduli stabilizations in the configuration of three magnetised intersecting D7 branes in the type-IIB/F theory, compactified on the 6d orbifold of Calabi-Yau three-fold (CY3). Two of the Kähler moduli are stabilized non-perturbatively, out of the three which get perturbative corrections up to one-loop–order multi-graviton scattering amplitudes in the large volume scenario. In this framework, the dS vacua are achieved through all Kähler moduli stabilizations by considering the D-term. We obtain inflaton potentials of slow-roll plateau type, which are expected by recent cosmological observations. Calculations of cosmological parameters with the potentials yield experimentally favoured values.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level.

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.