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The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces. [ABSTRACT FROM AUTHOR]

Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons. [ABSTRACT FROM AUTHOR]

Advances on variational approaches for the n-body problem in the past two decades have inspired recent investigations for the n-center problem. Substantial progress about periodic solutions within various homotopy classes has been made for n ≥ 3 . One technical tool in such investigations, the local deformation argument, plays an important role. A major challenge of this approach is to construct periodic orbits which have some lobes enclosing only one or two centers. Closer scrutiny for the two-center problem from variational perspectives is therefore essential for further developments in this direction. In this paper we consider the two-center problem and orbits of lemniscate type and planetary type. A lemniscate type orbit consists of two lobes with one center inside each lobe, and a planetary type orbit encloses both centers. We show the existence and minimizing property of planetary type periodic solutions for any given masses of centers at fixed positions, and the period can be arbitrary as long as it is above a mass-dependent threshold value. In contrast, numerical evidence suggests that lemniscate type orbits have higher action values than some homoclinic ejection-collision solutions. [ABSTRACT FROM AUTHOR]

Cosmological N-body simulation is associated with hyper-scale and high-resolution computing, and time will increase exponentially as the scale increases, which is always the most important issue that needs to be considered in N-body problems. With the increasing computing scale demand, high-performance computing systems and effective parallel algorithms have been applied to solve the N-body problem. PHotoNs-2, a parallel N-body simulation code designed for Lambda cold dark matter modelled simulation, was developed using the hybrid fast multipole method and particle-mesh method. In this study, PHotoNs-2 is migrated on a parallel heterogeneous CPU+Accelerator platform, which is referred to as PhotoNs-MA, and challenges are imposed on its performance by the massive data transmission, memory access, and complex mathematical functions. In this paper, the main optimizations for the kernel functions of short-range force calculations on the SIMT architecture are listed as follows: transmission of large amounts of data using page-locked memory and the structure of array to improve the efficiency of memory access, the transmission of index lists instead of particle interaction lists to reduce the transfer overhead, and using the interpolation method to replace the modified formula for interaction forces. Finally, compared with PHotoNs-2 run on 4 CPU cores, the optimized PHotoNs-MA on 4 accelerators accelerates the P2P operator 1000x times. We compared the results with Gadget-2 run on 64 CPU cores, and the overall performance is improved by 6 times for 4 accelerators. As for large-scale simulations, near-linear scalability is observed in P2P, and the parallel efficiency ultimately reaching 89.28%. [ABSTRACT FROM AUTHOR]

The influence of the variability of the masses of celestial bodies on the dynamic evolution of planetary systems is investigated in the case when the masses of the bodies change isotropically at different rates, and the laws of mass change are assumed to be arbitrary given functions of time. The classical problem of n + 1 bodies of variable mass when bodies move around a central star in quasi-elliptic nonintersecting orbits and interact according to the law of universal gravitation is used as a model of multi-planet system. Differential equations of body motion in terms of the osculating elements of aperiodic motion in quasi-conic sections are derived. An algorithm for calculating the perturbing function in the form of power series in small parameters and the derivation of differential equations determining the secular perturbations of the orbital elements are discussed. All symbolic computations are carried out using the computer algebra system Wolfram Mathematica. [ABSTRACT FROM AUTHOR]

Four small moons (Styx, Nix, Kerberos and Hydra) are at present known to orbit around the barycenter of Pluto and Charon, which are themselves considered a binary dwarf planet due to their relatively high mass ratio. The central, non-axisymmetric potential induces moon orbits inconvenient to be described by Keplerian osculating elements. Here, we report that observed orbital variations may not be the result of orbital eccentricities or observational uncertainties, but may be due to forced oscillations caused by the central binary. We show, using numerical integration and analytical considerations, that the differences reported on their orbital elements may well arise from this intrinsic behavior rather than limitations on our instruments. [ABSTRACT FROM AUTHOR]

We consider central configurations of the strictly spatial five-body problem with a homogeneous potential which are equilateral chains, i.e., configurations with four sequential equilateral edges containing all five vertices. First, we prove that any such configuration must be a triangular bipyramid with an equilateral triangle base. Furthermore, we show that the masses located at the vertices of the triangle must be equal and the masses of the other two particles which are off the base also must be equal. We also found that a particular triangular bipyramid configuration with fixed masses is a central configuration for a range of homogenous potentials generalizing the Newtonian potential. Finally, we conclude that there is a unique triangular bipyramid central configuration with equal masses for these same homogenous potentials. [ABSTRACT FROM AUTHOR]

Variational methods have been successfully applied to construct many different classes of periodic solution of N-body problem and N-center problem. However, until now, it is still challenging to apply variational methods to restricted (N + 1) -body problem. In this paper, we consider the restricted few-body-few-center problem (an intermediate problem between restricted (N + 1) -body problem and N-center problem) with symmetric torque-free primaries, identify its binary-syzygy sequence that can be realized by minimizers of the Lagrangian action functional, and construct its periodic solutions within certain topological classes. At the end, we further reveal similar results for restricted (N + 1) -body problem with the general rhomboidal primary system. In order to achieve the above aim, we also demonstrate the asymptotic behavior of the massless particle near two-body collision with a moving primary and establish partial Sundman–Sperling estimates of the massless particle near multi-body collision. [ABSTRACT FROM AUTHOR]

We provide new insight into the analysis of N-body problems by studying a compactification M N of R 3 N that is compatible with the analytic properties of the N-body Hamiltonian H N . We show that our compactification coincides with a compactification introduced by Vasy using blow-ups in order to study the scattering theory of N-body Hamiltonians and with a compactification introduced by Georgescu using C ∗ -algebras. In particular, the compactifications introduced by Georgescu and by Vasy coincide (up to a homeomorphism that is the identity on R 3 N ). Our result has applications to the spectral theory of N-body problems and to some related approximation properties. For instance, results about the essential spectrum, the resolvents, and the scattering matrices of H N (when they exist) may be related to the behavior near M N \ R 3 N (i.e., "at infinity") of their distribution kernels, which can be efficiently studied using our methods. The compactification M N is compatible with the action of the permutation group S N , which allows to implement bosonic and fermionic (anti-)symmetry relations. We also indicate how our results lead to a regularity result for the eigenfunctions of H N . [ABSTRACT FROM AUTHOR]

In the context of the Newtonian N-body problem, we prove the existence of a partially hyperbolic motion with prescribed positive energy and any initial collisionless configuration. Moreover, it is a free time minimizer of the respective supercritical Newtonian action or equivalently a geodesic ray for the respective Jacobi-Maupertuis metric. [ABSTRACT FROM AUTHOR]

There are multipartite entangled states in many-body systems which may be potential resources in various quantum applications. In this paper, based on clustering theorems, we show that both the gapped ground state and thermal state at an upper-bounded inverse temperature have no genuine multipartite nonlocality when disjoint regions are far away from each other. The present n-particle system shows only biseparable quantum correlations when the propagation relations show exponential decay. Similar result holds for spin systems with product states as initial states. These results show interesting features of quantum many-body systems with exponential decay of correlations. [ABSTRACT FROM AUTHOR]

L. Y. Jia recently proposed an algorithm that applies the variational method directly to coherent-pair condensates (VDPC) [L. Jia, Phys. Rev. C (2019).] Now I'll make changes to the VDPC algorithm that applies it to the Constraint Hatree–Fock theory. I derived expressions of the mean energy extremum with linear constraints and the analytic form of the Lagrangian multiplier. In addition, I acquire an angle through the inverse tangent of the energy minimum to the electric quadrupole moment in Fig. 3, which describes the unconstrained energy under an equivalent rotating system. I demonstrate the new algorithm in a semirealistic example using the realistic V low − k interaction in the large model spaces (up to 15 harmonic-oscillator major shells). In this work, I am interested in a wave function | ψ (Q) 〉 , which minimizes the total energy under the constraint that has a fixed expectation Q = 〈 ψ | Q ̂ | ψ 〉. I graphed the results as just an energy extreme versus electric quadrupole moment graph. The result shows that Fig. 3 is similar to Fig. 7.2 in [P. Ring and P. Schuck, The Nuclear Many-body Problem (Springer Science & Business Media, 2004)]. [ABSTRACT FROM AUTHOR]

Numerical integrations of the Solar system have been carried out for decades. Their results have been used, for example to determine whether the Solar system is chaotic, whether Mercury's orbit is stable, or to help discern Earth's climate history. We argue that all of the past studies we consider in this work are affected by numerical chaos to different degrees, affecting the possible orbits and instability probability of Mercury, sometimes significantly. We show how to eliminate the effects of numerical chaos by resolving Mercury's pericentre passage. We also show that several higher order symplectic maps do not exhibit significant differences in resolving pericentre passage of Mercury (at fixed time-step), making their advantages suspect for calculating long-term orbits. Resolving pericentre passage affects a wide array of orbital numerical studies, like exoplanet studies, studies of the galactic centre, and other N -body problems. [ABSTRACT FROM AUTHOR]

The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order n requires analyzing (if not solving) the quantum n-body problem. In this work, we present a comprehensive review of automated algebra methods, which we developed to calculate high-order virial coefficients. The methods are computational but non-stochastic, thus avoiding statistical effects; they are also for the most part analytic, not numerical, and amenable to massively parallel computer architectures. We show formalism and results for coefficients characterizing the thermodynamics (pressure, density, energy, static susceptibilities) of homogeneous and harmonically trapped systems and explain how to generalize them to other observables such as the momentum distribution, Tan contact, and the structure factor. [ABSTRACT FROM AUTHOR]

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system's Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments. Applying the language of computational complexity to study real-world experiments requires a rigorous framework. Here, the authors provide such a framework and establish that there can be an exponential savings in resources if an experimentalist can entangle apparatuses with experimental samples. [ABSTRACT FROM AUTHOR]

We introduce an algebraic method to study local stability in the Newtonian n -body problem when certain symmetries are present. We use representation theory of groups to simplify the calculations of certain eigenvalue problems. The method should be applicable in many cases, we give two main examples here: the square central configurations with four equal masses, and the equilateral triangular configurations with three equal masses plus an additional mass of arbitrary size at the center. Using representation theory of finite groups, we explicitly found the eigenvalues of certain 8 × 8 Hessians in these examples, with only some simple calculations of traces. We also studied the local stability properties of corresponding relative equilibria in the four-body problems. [ABSTRACT FROM AUTHOR]

For the Newtonian N-body problem, we study the Jacobi–Maupertuis metric of the nonnegative energy levels. We show that the geodesic rays are expansive, that is to say, all the distances between the bodies must be divergent functions. More precisely, we prove that the evolution of such motions asymptotically decomposes into free particles and subsystems in completely parabolic expansion. The theorem applies, in particular, to the maximal characteristic curves of any given global viscosity solution of the stationary Hamilton–Jacobi equation H (x , d x u) = h . [ABSTRACT FROM AUTHOR]

We prove that all non-degenerate relative equilibria of the planar Newtonian n –body problem can be continued to spaces of constant curvature κ , positive or negative, for small enough values of this parameter. We also compute the extension of some classical relative equilibria to curved spaces using numerical continuation. In particular, we extend Lagrange's triangle configuration with different masses to both positive and negative curvature spaces. [ABSTRACT FROM AUTHOR]

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green's function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0) of the ADG code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei. [ABSTRACT FROM AUTHOR]

As a follow-up of a previous work of the authors, this work considers uniform global time-renormalization functions for the gravitationalN-body problem. It improves on the estimates of the radii of convergence obtained therein by using a completely different technique, both for the solution to the original equations and for the solution of the renormalized ones. The aforementioned technique which the new estimates are built upon is known as majorants and allows for an easy application of simple operations on power series. The new radii of convergence so-obtained are approximately doubled with respect to our previous estimates. In addition, we show that majorants may also be constructed to estimate the local error of the implicit midpoint rule (and similarly for Runge-Kutta methods) when applied to the time-renormalized N-body equations and illustrate the interest of our results for numerical simulations of the Solar System. [ABSTRACT FROM AUTHOR]

In this paper, we consider central configurations of the planar 3n-body problem consisting of n masses at the vertices of a regular n-gon inscribed in a circle of radius r and 2n masses at the vertices of a second (not necessarily regular) concentric 2n-gon inscribed in a circle of radius ar which are symmetric in the sense that the set of positions of the 3n masses and the set of the corresponding masses are invariant under the action of a finite subgroup of O(2). There are two different types of such configurations. In the first type, called regular bicircular central configurations of the 3n-body problem, the second 2n-gon is regular, n of the vertices of the second n-gon are aligned with the vertices of the first regular n-gon and the masses at the vertices of this 2n-gon alternate values. In the second type, called semiregular bicircular central configurations of the 3n-body problem, the second 2n-gon is semiregular and the masses at its vertices are all of them equal. A semiregular 2n-gon has n pair of vertices symmetric by a reflection of an angle β with respect to the axis of symmetry of the first regular n-gon. Our aim is to analyze the set of values of the parameter a for the regular 2n-gon and of the parameters (a , β) for the semiregular 2n-gon providing symmetric bicircular central configurations. In particular, for all n ≥ 2 we prove analytically the existence of symmetric bicircular central configurations with a (respectively (a , β) ) satisfying some particular conditions. Using either computer-assisted results or numerical results, we also describe the complete set of values of a (respectively (a , β) ) providing symmetric bicircular central configurations for n = 2 , 3 , 4 , 5 and we give numerical evidences that the pattern for n > 5 is the same as the one for n = 5 . [ABSTRACT FROM AUTHOR]

In contrast to bound states, electronically metastable states or resonances still represent a major challenge for quantum chemistry and molecular physics. The reason lies in the embedding continuum: Bound states represent a many-body problem, while resonances represent a simultaneous scattering and many-body problem. Here we focus on so-called L 2 -methods, which treat the continuum only implicitly, but rather take the 'decaying state' perspective and emphasize electron correlation in the decaying state. These methods represent a natural extension of quantum chemistry into the metastable domain and are suitable for, say, modeling electron-induced reactions or resonant photo detachment. The three workhorse L 2 -methods are complex absorbing potentials, the stabilization method, and regularized analytic continuation. However, even for these three methods, making comparisons is less than straightforward as each method works best with a unique blend of electronic structure methods and basis sets. Here we address this issue by considering a model potential. For a model, we can establish a reliable reference resonance energy by using the complex scaling method and a discrete variable representation. Then, we can study the performance of the three workhorse methods as well as effects of more approximate Gaussian basis sets. [ABSTRACT FROM AUTHOR]

For each given n ≥ 2 , we study the variational existence of a new spatial periodic orbit in the 2n-body problem. Besides excluding possible collision singularities, the main challenges left are to show that the orbit is not a relative equilibrium and it is spatial. By introducing a new estimate in the collinear central configuration, we can prove that it is not a relative equilibrium in the 2n-body problem. Furthermore, with the help of numerical calculation, the orbit is spatial in the equal-mass four-body problem. [ABSTRACT FROM AUTHOR]

Although the many-body expansion (MBE) approach is widely applied to estimate the energy of large systems containing weak interactions, it is inapplicable to calculating the energies of covalent or metal clusters. In this work, we propose an interaction many-body expansion (IMBE) to calculate the energy of atomic clusters containing covalent bonds. In this approach, the energy of a system is expressed as the sum of the energy of atoms and the interaction energy between the atom and its surrounding atoms. The IMBE method is first applied to calculate the energies of nitrogen clusters, in which the interatomic interactions are truncated to four-body terms. The results show that the IMBE approach could significantly reduce the energy error for nitrogen clusters compared with the traditional MBE method. The weak size and structure dependence of the IMBE error with respect to DFT calculations indicates the IMBE method has good potential application in estimating energy of large covalent systems. [ABSTRACT FROM AUTHOR]

In the present contribution, the ultrafast photoinduced electron migration dynamics at the interface between an alizarin dye and an anatase TiO2 thin film is investigated from first principles. Comparison between a time-dependent many-electron configuration interaction ansatz and a single active electron approach sheds light on the importance of many-body effects, stemming from uniquely defined initial conditions prior to photoexcitation. Particular emphasis is put on understanding the influence of the binding mode on the migration process. The dynamics is analyzed on the basis of a recently introduced toolset in the form of electron yields, electronic fluxes, and flux densities, to reveal microscopic details of the electron migration mechanism. From the many-body perspective, insight into the nature of electron-electron and hole-hole interactions during the charge transfer process is obtained. The present results reveal that the single active electron approach yields quantitatively and phenomenologically similar results as the many-electron ansatz. Furthermore, the charge migration processes in the dye-TiO2 model clusters with different binding modes exhibit similar mechanistic pathways but on largely different time scales. [ABSTRACT FROM AUTHOR]

Charged dielectric spheres embedded in a dielectric medium provide the simplest model for manybody systems of polarizable ions and charged colloidal particles. We provide a multiple scattering formulation for the total electrostatic energy for such systems and demonstrate that the polarization energy can be rapidly evaluated by an image method that generalizes the image methods for conducting spheres. Individual contributions to the total electrostatic energy are ordered according to the number of polarized surfaces involved, and each additional surface polarization reduces the energy by a factor of (a/R)³∊, where a is the sphere radius, R the average inter-sphere separation, and ∊ the relevant dielectric mismatch at the interface. Explicit expressions are provided for both the energy and the forces acting on individual spheres, which can be readily implemented in Monte Carlo and molecular dynamics simulations of polarizable charged spheres, thereby avoiding costly computational techniques that introduce a surface charge distribution that requires numerical solution. [ABSTRACT FROM AUTHOR]

In modern physics and chemistry concerned with many-body systems, one of the mainstays is identical-particle-permutation symmetry. In particular, both the intra-molecular dynamics of a single molecule and the inter-molecular dynamics associated, for example, with reactive molecular collisions are strongly affected by selection rules originating in nuclear-permutation symmetry operations being applied to the total internal wavefunctions, including nuclear spin, of the molecules involved. We propose here a general tool to determine coherently the permutation symmetry and the rotational symmetry (associated with the group of arbitrary rotations of the entire molecule in space) of molecular wavefunctions, in particular the nuclear-spin functions. Thus far, these two symmetries were believed to be mutually independent and it has even been argued that under certain circumstances, it is impossible to establish a one-to-one correspondence between them. However, using the Schur-Weyl duality theorem we show that the two types of symmetry are inherently coupled. In addition, we use the ingenious representation-theory technique of Young tableaus to represent the molecular nuclear-spin degrees of freedom in terms of well-defined mathematical objects. This simplifies the symmetry classification of the nuclear wavefunction even for large molecules. Also, the application to reactive collisions is very straightforward and provides a much simplified approach to obtaining selection rules. [ABSTRACT FROM AUTHOR]

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct computational evaluation requires O(N2) operations, where N is the number of unknowns. Such a scaling, which arises from the many-body nature of the relevant Green's function, has precluded wide-spread adoption of integral methods for solution of large-scale scientific and engineering problems. In this work, a parallel computational approach is presented that relies on using scalable open source libraries and utilizes a kernel-independent Fast Multipole Method (FMM) to evaluate the integrals in O(N) operations, with O(N) memory cost, thereby substantially improving the scalability and efficiency of computational integral methods. We demonstrate the accuracy, efficiency, and scalability of our approach in the context of two examples. In the first, we solve a boundary value problem for a ferroelectric/ferromagnetic volume in free space. In the second, we solve an electrostatic problem involving polarizable dielectric bodies in an unbounded dielectric medium. The results from these test cases show that our proposed parallel approach, which is built on a kernel-independent FMM, can enable highly efficient and accurate simulations and allow for considerable flexibility in a broad range of applications. [ABSTRACT FROM AUTHOR]

We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced flexible adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examples of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave function methods to sizable, covalently bound systems. [ABSTRACT FROM AUTHOR]

Due to the importance of both static and dynamical correlation in the bond formation, lowdimensional beryllium systems constitute interesting case studies to test correlation methods. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. To gain insight into the main characteristics of the wave function, we started by focusing on the description of small Be chains using standard quantum chemical methods. In a next step we applied the MoI to larger beryllium systems, starting from the Be6 ring. The complete active space formalism was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Although this is a wellestablished approach for systems with limited multireference character, its application regarding the description of whole dissociation curves requires further testing. Subsequent to the discussion of the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain. [ABSTRACT FROM AUTHOR]

We have implemented the polarizable continuum model within the framework of the many-body Green's function GW formalism for the calculation of electron addition and removal energies in solution. The present formalism includes both ground-state and non-equilibrium polarization effects. In addition, the polarization energies are state-specific, allowing to obtain the bath-induced renormalisation energy of all occupied and virtual energy levels. Our implementation is validated by comparisons with ΔSCF calculations performed at both the density functional theory and coupledcluster single and double levels for solvated nucleobases. The present study opens the way to GW and Bethe-Salpeter calculations in disordered condensed phases of interest in organic optoelectronics, wet chemistry, and biology. [ABSTRACT FROM AUTHOR]

To complement our study of the role of finite precision in electronic structure calculations based on a truncated many-body expansion (MBE, or "n-body expansion"), we examine the accuracy of such methods in the present work. Accuracy may be defined either with respect to a supersystem calculation computed at the same level of theory as the n-body calculations, or alternatively with respect to high-quality benchmarks. Both metrics are considered here. In applications to a sequence of water clusters, (H2O)N=6-55 described at the B3LYP/cc-pVDZ level, we obtain mean absolute errors (MAEs) per H2O monomer of ~1.0 kcal/mol for two-body expansions, where the benchmark is a B3LYP/cc-pVDZ calculation on the entire cluster. Three- and four-body expansions exhibit MAEs of 0.5 and 0.1 kcal/mol/monomer, respectively, without resort to charge embedding. A generalized many-body expansion truncated at two-body terms [GMBE(2)], using 3-4 H2O molecules per fragment, outperforms all of these methods and affords a MAE of ~0.02 kcal/mol/monomer, also without charge embedding. GMBE(2) requires significantly fewer (although somewhat larger) subsystem calculations as compared to MBE(4), reducing problems associated with floating-point roundoff errors. When compared to high-quality benchmarks, we find that error cancellation often plays a critical role in the success of MBE(n) calculations, even at the four-body level, as basis-set superposition error can compensate for higher-order polarization interactions. A many-body counterpoise correction is introduced for the GMBE, and its two-body truncation [GMBCP(2)] is found to afford good results without error cancellation. Together with a method such as ωB97X-V/aug-cc-pVTZ that can describe both covalent and non-covalent interactions, the GMBE(2)+GMBCP(2) approach provides an accurate, stable, and tractable approach for large systems. [ABSTRACT FROM AUTHOR]

We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out from its environment, while the entire system (atom and environment) is described by a Slater determinant or its antisymmetrized geminal power (AGP) extension. The embedding procedure described here allows for the systematic and consistent contraction of the primitive basis set into geminal embedded orbitals (GEOs), with a dramatic reduction of the number of variational parameters necessary to represent the many-body wave function, for a chosen target accuracy. Within the variational Monte Carlo method, the Slater or AGP part is determined by a variational minimization of the energy of the whole system in presence of a flexible and accurate Jastrow factor, representing most of the dynamical electronic correlation. The resulting GEO basis set opens the way for a fully controlled optimization of many-body wave functions in electronic structure calculation of bulk materials, namely, containing a large number of electrons and atoms. We present applications on the water molecule, the volume collapse transition in cerium, and the high-pressure liquid hydrogen. [ABSTRACT FROM AUTHOR]

The present work investigates the capability of bottom-up coarse-graining (CG) methods for accurately modeling both structural and thermodynamic properties of all-atom (AA) models for molecular liquids. In particular, we consider 1, 2, and 3-site CG models for heptane, as well as 1 and 3-site CG models for toluene. For each model, we employ the multiscale coarse-graining method to determine interaction potentials that optimally approximate the configuration dependence of the many-body potential of mean force (PMF). We employ a previously developed "pressure-matching" variational principle to determine a volume-dependent contribution to the potential,UV(V), that approximates the volume-dependence of the PMF. We demonstrate that the resulting CG models describe AA density fluctuations with qualitative, but not quantitative, accuracy. Accordingly, we develop a self-consistent approach for further optimizing UV, such that the CG models accurately reproduce the equilibrium density, compressibility, and average pressure of the AA models, although the CG models still significantly underestimate the atomic pressure fluctuations. Additionally, by comparing this array of models that accurately describe the structure and thermodynamic pressure of heptane and toluene at a range of different resolutions, we investigate the impact of bottom-up coarse-graining upon thermodynamic properties. In particular, we demonstrate that UV accounts for the reduced cohesion in the CG models. Finally, we observe that bottom-up coarse-graining introduces subtle correlations between the resolution, the cohesive energy density, and the "simplicity" of the model. [ABSTRACT FROM AUTHOR]

By eliminating unnecessary degrees of freedom, coarse-grained (CG) models tremendously facilitate numerical calculations and theoretical analyses of complex phenomena. However, their success critically depends upon the representation of the system and the effective potential that governs the CG degrees of freedom. This work investigates the relationship between the CG representation and the many-body potential of mean force (PMF), W, which is the appropriate effective potential for a CG model that exactly preserves the structural and thermodynamic properties of a given high resolution model. In particular, we investigate the entropic component of the PMF and its dependence upon the CG resolution. This entropic component, SW, is a configuration-dependent relative entropy that determines the temperature dependence of W. As a direct consequence of eliminating high resolution details from the CG model, the coarsening process transfers configurational entropy and information from the configuration space into SW. In order to further investigate these general results, we consider the popular Gaussian Network Model (GNM) for protein conformational fluctuations. We analytically derive the exact PMF for the GNM as a function of the CG representation. In the case of the GNM, -TSW is a positive, configuration-independent term that depends upon the temperature, the complexity of the protein interaction network, and the details of the CG representation. This entropic term demonstrates similar behavior for seven model proteins and also suggests, in each case, that certain resolutions provide a more efficient description of protein fluctuations. These results may provide general insight into the role of resolution for determining the information content, thermodynamic properties, and transferability of CG models. Ultimately, they may lead to a rigorous and systematic framework for optimizing the representation of CG models. [ABSTRACT FROM AUTHOR]

The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as meanfield approaches replace detailed interactions with averaged approximations. However, long-range coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16-29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375-400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1-29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction φ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ φ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to φ ≤ 0.4, the relative mobility does not reached the far-field value even beyond separations of many particle sizes. In the case of φ = 0.5, the far-field asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquid-like structural effects on pair mobility at close separations. These results confirm that long-range many-body hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes. [ABSTRACT FROM AUTHOR]

We consider the critical points (equilibria) of a planar potential generated by n Newtonian point masses augmented with a quadratic term (such as arises from a centrifugal effect). Particular cases of this problem have been considered previously in studies of the circular-restricted n-body problem. We show that the number of equilibria is finite for a generic set of parameters, and we establish estimates for the number of equilibria. We prove that the number of equilibria is bounded below by n + 1, and we provide examples to show that this lower bound is sharp. We prove an upper bound on the number of equilibria that grows exponentially in n. In order to establish a lower bound on the maximum number of equilibria, we analyze a class of examples, referred to as "ring configurations," consisting of n − 1 equal masses positioned at vertices of a regular polygon with an additional mass located at the center. Previous numerical observations indicate that these configurations can produce as many as 5n − 5 equilibria. We verify analytically that the ring configuration has at least 5n − 5 equilibria when the central mass is sufficiently small. We conjecture that the maximum number of equilibria grows linearly with the number of point masses. We also discuss some mathematical similarities to other equilibrium problems in mathematical physics, namely, Maxwell's problem from electrostatics and the image counting problem from gravitational lensing. [ABSTRACT FROM AUTHOR]

Free-surface fluid dynamics at the nanoscale is shown to strongly depend on thermal fluctuations. These fluctuations can be predicted by particle-based models numerically and analyzed by stochastic partial differential equations theoretically. In this work, we employ one of the particle methods, known as many-body dissipative particle dynamics (mDPD), to investigate the influence of thermal fluctuations on nanoscale free-surface flows. After enough independent simulations are performed for convincing ensemble-averaged results, mDPD not only shows good consistency with theories derived from the Landau–Lifshitz Navier–Stokes equations, but also indicates high efficiency in contrast with traditional molecular dynamics (MD). These results confirm that mDPD has capabilities of capturing the physics of fluctuating hydrodynamics in nanoscale free-surface flows, especially the complicated three-dimensional behaviors that cannot be predicted by theoretical models, both accurately and efficiently. [ABSTRACT FROM AUTHOR]

A normal ordered exponential parametrisation is used to obtain equations for thermal one-and two-particle reduced density matrices, as well as free energies, partition functions and entropy for both Fermionic (electronic) and Bosonic (vibrational) Hamiltonians. A first principles derivation of the equations, relying only on a simple Wick's theorem and starting from the differential equation d D ^ d β = − (H ^ − μ N ^) D ^ , is presented that yields a differential equation for the amplitudes representing density cumulants, as well as the grand potential. In contrast to other approaches reported in the literature, the theory does not use the interaction picture and an integral formulation as a starting point but rather requires a propagation of the resulting differential equation for the amplitudes in the Schrödinger representation. While the theory is applicable to general classes of many-body problems in principle, here, the theory is illustrated using simple model systems. As an application of the related time-dependent formulation numerically exact time-autocorrelation functions and absorption spectra are obtained for harmonic Franck–Condon problems. These examples illustrate the basic soundness of the scheme and are used for pedagogical purposes. Other approaches in the literature are only discussed briefly and no detailed comparative discussion is attempted. [ABSTRACT FROM AUTHOR]