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.

Helical Organic and Inorganic Polymers.

Despite being a staple of synthetic plastics and biomolecules, helical polymers are scarcely studied with Gaussian-basis-set ab initio electron-correlated methods on an equal footing with molecules. This article introduces an ab initio second-order many-body Green's function [MBGF(2)] method with nondiagonal, frequency-dependent Dyson self-energy for infinite helical polymers using screw-axis-symmetry-adapted Gaussian-spherical-harmonics basis functions. Together with the Gaussian-basis-set density-functional theory for energies, analytical atomic forces, translational-period force, and helical-angle force, it can compute correlated energy, quasiparticle energy bands, structures, and vibrational frequencies of an infinite helical polymer, which smoothly converge at the corresponding oligomer results. These methods can handle incommensurable structures, which have an infinite translational period and are hard to characterize by any other method, just as efficiently as commensurable structures. We apply them to polyethylene (2/1 helix), polyacetylene (Peierls' system) and polytetrafluoroethylene (13/6 helix) to establish the quantitative accuracy of MBGF(2)/cc-pVDZ in simulating their (angle-resolved) ultraviolet photoelectron spectra and of B3LYP/cc-pVDZ or 6-31G** in reproducing their structures, infrared and Raman band positions, phonon dispersions, and (coherent and incoherent) inelastic neutron scattering spectra. We then predict the same properties for infinitely catenated chains of nitrogen or oxygen and discuss their possible metastable existence under ambient conditions. They include planar zigzag polyazene (N2)x (Peierls' system), 11/3-helical isotactic polyazane (NH)x, 9/4-helical isotactic polyfluoroazane (NF)x, and 7/2-helical polyoxane (O)x as potential high-energy-density materials.

Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method.

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-cumulative distribution function method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with 92% strong scalability going from 64 to 4096 processors.

Intestinal microbe-dependent ω3 lipid metabolite αKetoA prevents inflammatory diseases in mice and cynomolgus macaques.

Dietary ω3 fatty acids have important health benefits and exert their potent bioactivity through conversion to lipid mediators. Here, we demonstrate that microbiota play an essential role in the body's use of dietary lipids for the control of inflammatory diseases. We found that amounts of 10-hydroxy-cis-12-cis-15-octadecadienoic acid (αHYA) and 10-oxo-cis-12-cis-15-octadecadienoic acid (αKetoA) increased in the feces and serum of specific-pathogen-free, but not germ-free, mice when they were maintained on a linseed oil diet, which is high in α-linolenic acid. Intake of αKetoA, but not αHYA, exerted anti-inflammatory properties through a peroxisome proliferator-activated receptor (PPAR)γ-dependent pathway and ameliorated hapten-induced contact hypersensitivity by inhibiting the development of inducible skin-associated lymphoid tissue through suppression of chemokine secretion from macrophages and inhibition of NF-κB activation in mice and cynomolgus macaques. Administering αKetoA also improved diabetic glucose intolerance by inhibiting adipose tissue inflammation and fibrosis through decreased macrophage infiltration in adipose tissues and altering macrophage M1/M2 polarization in mice fed a high-fat diet. These results collectively indicate that αKetoA is a novel postbiotic derived from α-linolenic acid, which controls macrophage-associated inflammatory diseases and may have potential for developing therapeutic drugs as well as probiotic food products.

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles.

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh-Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams-renormalization diagrams-whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. The normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree-Fock and first-order many-body perturbation theories.

Monte Carlo MP2-F12 for Noncovalent Interactions: The C60 Dimer.

A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green's functions in real space and imaginary time. These integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol-1 for the C60 dimer at the center distance of 9.748 Å.

12-Hydroxyeicosapentaenoic acid inhibits foam cell formation and ameliorates high-fat diet-induced pathology of atherosclerosis in mice.

Atherosclerosis is a chronic inflammatory disease associated with macrophage aggregate and transformation into foam cells. In this study, we sought to investigate the impact of dietary intake of ω3 fatty acid on the development of atherosclerosis, and demonstrate the mechanism of action by identifying anti-inflammatory lipid metabolite. Mice were exposed to a high-fat diet (HFD) supplemented with either conventional soybean oil or α-linolenic acid-rich linseed oil. We found that as mice became obese they also showed increased pulsatility and resistive indexes in the common carotid artery. In sharp contrast, the addition of linseed oil to the HFD improved pulsatility and resistive indexes without affecting weight gain. Histological analysis revealed that dietary linseed oil inhibited foam cell formation in the aortic valve. Lipidomic analysis demonstrated a particularly marked increase in the eicosapentaenoic acid-derived metabolite 12-hydroxyeicosapentaenoic acid (12-HEPE) in the serum from mice fed with linseed oil. When we gave 12-HEPE to mice with HFD, the pulsatility and resistive indexes was improved. Indeed, 12-HEPE inhibited the foamy transformation of macrophages in a peroxisome proliferator-activated receptor (PPAR)γ-dependent manner. These results demonstrate that the 12-HEPE-PPARγ axis ameliorates the pathogenesis of atherosclerosis by inhibiting foam cell formation.

Stochastic evaluation of fourth-order many-body perturbation energies.

A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green's functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n5.3) size-dependence of cost, which is nearly two ranks lower than the O(n7) dependence of the deterministic MP4 algorithm. It evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mEh (1.1% of the total basis-set correlation energy), 38 mEh (2.6%), 110 mEh (5.5%), and 280 mEh (9.0%), respectively, after about 109 MC steps.

ω3 fatty acid metabolite, 12-hydroxyeicosapentaenoic acid, alleviates contact hypersensitivity by downregulation of CXCL1 and CXCL2 gene expression in keratinocytes via retinoid X receptor α.

ω3 fatty acids show potent bioactivities via conversion into lipid mediators; therefore, metabolism of dietary lipids is a critical determinant in the properties of ω3 fatty acids in the control of allergic inflammatory diseases. However, metabolic progression of ω3 fatty acids in the skin and their roles in the regulation of skin inflammation remains to be clarified. In this study, we found that 12-hydroxyeicosapentaenoic acid (12-HEPE), which is a 12-lipoxygenase metabolite of eicosapentaenoic acid, was the prominent metabolite accumulated in the skin of mice fed ω3 fatty acid-rich linseed oil. Consistently, the gene expression levels of Alox12 and Alox12b, which encode proteins involved in the generation of 12-HEPE, were much higher in the skin than in the other tissues (eg, gut). We also found that the topical application of 12-HEPE inhibited the inflammation associated with contact hypersensitivity by inhibiting neutrophil infiltration into the skin. In human keratinocytes in vitro, 12-HEPE inhibited the expression of two genes encoding neutrophil chemoattractants, CXCL1 and CXCL2, via retinoid X receptor α. Together, the present results demonstrate that the metabolic progression of dietary ω3 fatty acids differs in different organs, and identify 12-HEPE as the dominant ω3 fatty acid metabolite in the skin.

Anharmonic Phonon Dispersion in Polyethylene.

The second-order Green's function method for anharmonic crystals has been applied to an infinite, periodic chain of polyethylene taking into account up to quartic force constants. The frequency-independent approximation to the Dyson self-energy gives rise to numerous divergent resonances, which are fortuitous. Instead, solving the Dyson equation self-consistently with a frequency-dependent self-energy resists divergences from resonances or zero-frequency acoustic vibrations. The calculated anharmonic phonon dispersion, which nonetheless displays many true resonances, and anharmonic phonon density of states furnish hitherto unknown details that explain smaller features of observed vibrational spectra.

Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling.

In the Monte Carlo many-body perturbation (MC-MP) method, the conventional correlation-correction formula, which is a long sum of products of low-dimensional integrals, is first recast into a short sum of high-dimensional integrals over electron-pair and imaginary-time coordinates. These high-dimensional integrals are then evaluated by the Monte Carlo method with random coordinates generated by the Metropolis-Hasting algorithm according to a suitable distribution. The latter algorithm, while advantageous in its ability to sample nearly any distribution, introduces autocorrelation in sampled coordinates, which, in turn, increases the statistical uncertainty of the integrals and thus the computational cost. It also involves wasteful rejected moves and an initial "burn-in" step as well as displays hysteresis. Here, an algorithm is proposed that directly produces a random sequence of electron-pair coordinates for the same distribution used in the MC-MP method, which is free from autocorrelation, rejected moves, a burn-in step, or hysteresis. This direct-sampling algorithm is shown to accelerate second- and third-order Monte Carlo many-body perturbation calculations by up to 222% and 38%, respectively.

Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates.

The use of many control variates is proposed as a method to accelerate the second- and third-order Monte Carlo (MC) many-body perturbation (MC-MP2 and MC-MP3) calculations. A control variate is an exactly integrable function that is strongly correlated or anti-correlated with the target function to be integrated by the MC method. Evaluating both integrals and their covariances in the same MC run, one can effect a mutual cancellation of the statistical uncertainties and biases in the MC integrations, thereby accelerating its convergence considerably. Six and thirty-six control variates, whose integrals are known a priori, are generated for MC-MP2 and MC-MP3, respectively, by systematically replacing one or more two-electron-integral vertices of certain configurations by zero-valued overlap-integral vertices in their Goldstone diagrams. The variances and covariances of these control variates are computed at a marginal cost, enhancing the overall efficiency of the MC-MP2 and MC-MP3 calculations by a factor of up to 14 and 20, respectively.

Vitamin B1 Supports the Differentiation of T Cells through TGF-ß Superfamily Production in Thymic Stromal Cells.

Homeostatic generation of T cells, which occurs in the thymus, is controlled at least in part by endogenous cytokines and ligands. In addition, nutritional factors are other key regulators for the homeostasis of host immunity, but whether and how nutrition affects the homeostatic generation of thymocytes remains to be established. Here, we showed that vitamin B1 deficiency resulted in a bias toward the maturation of γδ thymocytes accompanied by decreased differentiation into double-positive thymocytes during thymic involution. These events were mediated through the increased production of TGF-ß superfamily members due to the accumulation of branched-chain α-keto acids in thymic stromal cells. These findings revealed essential roles of vitamin B1 in the appropriate differentiation of T cells through the metabolism of thymic stromal cells.

Finite-temperature many-body perturbation theory in the grand canonical ensemble.

A finite-temperature many-body perturbation theory is presented, which expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals analytical formulas for the second-order perturbation corrections to these thermodynamic properties are obtained in a time-independent, nondiagrammatic, algebraic derivation, relying on the sum rules of the Hirschfelder-Certain degenerate perturbation energies in a degenerate subspace as well as nine algebraic identities for the zeroth-order thermal averages of one- through four-indexed quantities and products thereof. They reproduce numerically exactly the benchmark data obtained as the numerical derivatives of the thermal-full-configuration-interaction results for a wide range of temperatures.

17(S),18(R)-epoxyeicosatetraenoic acid generated by cytochrome P450 BM-3 from Bacillus megaterium inhibits the development of contact hypersensitivity via G-protein-coupled receptor 40-mediated neutrophil suppression.

Dietary intake of ω3 polyunsaturated fatty acids such as eicosapentaenoic acid and docosahexaenoic acid is beneficial for health control. We recently identified 17,18-epoxyeicosatetraenoic acid (17,18-EpETE) as a lipid metabolite endogenously generated from eicosapentaenoic acid that exhibits potent anti-allergic and anti-inflammatory properties. However, chemically synthesized 17,18-EpETE is enantiomeric due to its epoxy group-17(S),18(R)-EpETE and 17(R),18(S)-EpETE. In this study, we demonstrated stereoselective differences of 17(S),18(R)-EpETE and 17(R),18(S)-EpETE in amelioration of skin contact hypersensitivity and found that anti-inflammatory activity was detected in 17(S),18(R)-EpETE, but not in 17(R),18(S)-EpETE. In addition, we found that cytochrome P450 BM-3 derived from Bacillus megaterium stereoselectively converts EPA into 17(S),18(R)-EpETE, which effectively inhibited the development of skin contact hypersensitivity by inhibiting neutrophil migration in a G protein-coupled receptor 40-dependent manner. These results suggest the new availability of a bacterial enzyme to produce a beneficial lipid mediator, 17(S),18(R)-EpETE, in a stereoselective manner. Our findings highlight that bacterial enzymatic conversion of fatty acid is a promising strategy for mass production of bioactive lipid metabolites.

Finite-temperature many-body perturbation theory in the canonical ensemble.

Benchmark data are presented for the zeroth- through third-order many-body perturbation corrections to the electronic Helmholtz energy, internal energy, and entropy in the canonical ensemble in a wide range of temperature. They are determined as numerical λ-derivatives of the respective quantities computed by thermal full configuration interaction with a perturbation-scaled Hamiltonian, H[over ̂]=H[over ̂]_{0}+λV[over ̂]. Sum-over-states analytical formulas for up to the third-order corrections to these properties are also derived as analytical λ-derivatives. These formulas, which are verified by exact numerical agreement with the benchmark data, are given in terms of the Hirschfelder-Certain degenerate perturbation energies and should be valid for both degenerate and nondegenerate reference states at any temperature down to zero. The results in the canonical ensemble are compared with the same in the grand canonical ensemble.

Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation.

A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed random walkers to the points of a uniform infinite spatial grid, allowing them to meet and annihilate one another to establish the nodal structure without the fixed-node approximation. An imaginary-time propagator is derived rigorously from a discretized Hamiltonian, governing a non-Gaussian, sign-flipping, branching, and mutually annihilating random walk of particles. The accuracy of the resulting stochastic representations of a fermion wave function is limited only by the grid and imaginary-time resolutions and can be improved in a controlled manner. The method is tested for a series of model problems including fermions in a harmonic trap as well as the He atom in its singlet or triplet ground state. For the latter case, the energies approach from above with increasing grid resolution and converge within 0.015E_{h} of the exact basis-set-limit value for the grid spacing of 0.08 a.u. with a statistical uncertainty of 10^{-5}E_{h} without an importance sampling or Jastrow factor.

Maternal ω3 docosapentaenoic acid inhibits infant allergic dermatitis through TRAIL-expressing plasmacytoid dendritic cells in mice.

BACKGROUND: Maternal dietary exposures are considered to influence the development of infant allergies through changes in the composition of breast milk. Cohort studies have shown that ω3 polyunsaturated fatty acids (PUFAs) in breast milk may have a beneficial effect on the preventing of allergies in infants; however, the underlying mechanisms remain to be investigated. We investigated how the maternal intake of dietary ω3 PUFAs affects fatty acid profiles in the breast milk and their pups and reduced the incidence of allergic diseases in the pups. METHODS: Contact hypersensitivity (CHS) induced by 2,4-dinitrofluorobenzene (DNFB) and fluorescein isothiocyanate was applied to the skin in pups reared by mother maintained with diets mainly containing ω3 or ω6 PUFAs. Skin inflammation, immune cell populations, and expression levels of immunomodulatory molecules in pups and/or human cell line were investigated by using flow cytometric, immunohistologic, and quantitative RT-PCR analyses. ω3 PUFA metabolites in breast milk and infant's serum were evaluated by lipidomics analysis using LC-MS/MS. RESULTS: We show that maternal intake of linseed oil, containing abundant ω3 α-linolenic acid, resulted in the increased levels of ω3 docosapentaenoic acid (DPA) and its 14-lipoxygenation products in the breast milk of mouse dams; these metabolites increased the expression of TNF-related apoptosis-inducing ligand (TRAIL) on plasmacytoid dendritic cells (pDCs) in their pups and thus inhibited infant CHS. Indeed, the administration of DPA-derived 14-lipoxygenation products to mouse pups ameliorated their DNFB CHS. CONCLUSION: These findings suggest that an inhibitory mechanism in infant skin allergy is induced through maternal metabolism of dietary ω3 PUFAs in mice.

Dietary Omega-3 Fatty Acid Dampens Allergic Rhinitis via Eosinophilic Production of the Anti-Allergic Lipid Mediator 15-Hydroxyeicosapentaenoic Acid in Mice.

The metabolism and generation of bioactive lipid mediators are key events in the exertion of the beneficial effects of dietary omega-3 fatty acids in the regulation of allergic inflammation. Here, we found that dietary linseed oil, which contains high amounts of alpha-linolenic acid (ALA) dampened allergic rhinitis through eosinophilic production of 15-hydroxyeicosapentaenoic acid (15-HEPE), a metabolite of eicosapentaenoic acid (EPA). Lipidomic analysis revealed that 15-HEPE was particularly accumulated in the nasal passage of linseed oil-fed mice after the development of allergic rhinitis with the increasing number of eosinophils. Indeed, the conversion of EPA to 15-HEPE was mediated by the 15-lipoxygenase activity of eosinophils. Intranasal injection of 15-HEPE dampened allergic symptoms by inhibiting mast cell degranulation, which was mediated by the action of peroxisome proliferator-activated receptor gamma. These findings identify 15-HEPE as a novel EPA-derived, and eosinophil-dependent anti-allergic metabolite, and provide a preventive and therapeutic strategy against allergic rhinitis.

Monte Carlo Second- and Third-Order Many-Body Green's Function Methods with Frequency-Dependent, Nondiagonal Self-Energy.

We fully develop the Monte Carlo many-body Green's function (MC-GF) method with the following enhancements: (1) The truncation order of the perturbation expansion of the Dyson self-energy is raised from the second order (MC-GF2) to the third order (MC-GF3) with the aid of a computerized procedure to enumerate and transform all 84 third-order Goldstone diagrams into Monte Carlo integrable expressions and then into central processing unit (CPU)/graphical processing unit (GPU)-parallel computer codes. (2) An efficient algorithm is proposed that computes all off-diagonal and diagonal elements of the MC-GF2 and MC-GF3 self-energy matrices by common subexpression elimination. (3) The frequency-independent approximation is lifted by introducing a method that computes frequency derivatives of the MC-GF2 and MC-GF3 self-energies up to any arbitrarily high order at nearly no additional computational cost. (4) The imaginary-time integration in the Laplace-transformed expressions of the self-energy is carried out stochastically (instead of using a quadrature in the previous implementations), resulting in a 50- to 200-fold speedup. (5) The efficiency of the redundant-walker convergence acceleration scheme is analyzed numerically, and the guidelines are established to select an optimal number of walkers for maximal efficiency. When such an optimal number is used, the cost per sample is constant of molecular size on either many CPUs or many GPUs. (6) The computational cost to obtain a binding energy within a given statistical uncertainty is observed to increase as (tentatively) O(n4) and O(n5) of molecular size (n is the number of electrons) with and without the diagonal approximation, respectively, as opposed to O(n5) and O(n6) of the corresponding deterministic algorithms. With this method applied to the electron binding energies of C60, we show that the third-order corrections to the self-energies are much greater in electron binding energies than in ground-state energies. They display a sign of oscillatory convergence toward experimental results, not necessarily improving the agreement with increasing perturbation order, justifying MC-GF3 and motivating even higher-order methods.