Two-body Corrections Research Articles

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe-Salpeter Equation.

Herein, we present a fragment-based approach for calculating the charged and neutral excited states in molecular systems, based on the many-body Green's function method within the GW approximation and the Bethe-Salpeter equation (BSE). The implementation relies on the many-body expansion of the total irreducible polarizability on the basis of fragment molecular orbitals. The GW quasi-particle energies in complex molecular environments are obtained by the GW calculation for the target fragment plus induced polarization contributions of the surrounding fragments at the static Coulomb-hole plus screened exchange level. In addition, we develop a large-scale GW/BSE method for calculating the delocalized excited states of molecular aggregates, based on the fragment molecular orbital method and the exciton model. The accuracy of fragment-based GW and GW/BSE methods was evaluated on molecular clusters and molecular crystals. We found that the accuracy of the total irreducible polarizability can be improved systematically by including two-body correction terms, and the fragment-based calculations can reasonably reproduce the results of the corresponding unfragmented calculations with a relative error of less than 100 meV. The proposed approach enables efficient excited-state calculations for large molecular systems with reasonable accuracy.

Tunneling matrix element and tunneling pathways of protein electron transfer calculated with a fragment molecular orbital method

Practical ways to calculate the tunneling matrix elements and analyze the tunneling pathways for protein electron-transfer (ET) reactions with a fragment molecular orbital (FMO) method are presented. The straightforward use of minimal basis sets only for the atoms involved in the covalent bond detachment in FMO can properly describe the ETs through the protein main-chains with the cost-effective two-body corrections (FMO2) without losing the quality of double-zeta basis sets. The current FMO codes have been interfaced with density functional theory, polarizable continuum model, and model core potentials, with which the FMO-based protein ET calculations can consider the effects of electron correlation, solvation, and transition-metal redox centers. The reasonable performance of the FMO-based ET calculations is demonstrated for three different sets of protein-ET model molecules: (1) hole transfer between two tryptophans covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, (2) ET between two plastoquinones covalently bridged by a polyalanine linker in the ideal α-helix and β-strand conformations, and (3) hole transfer between ruthenium (Ru) and copper (Cu) complexes covalently bridged by a stretch of a polyglycine linker as a model for Ru-modified derivatives of azurin.

Two-body corrections to the g factors of the bound muon and nucleus in light muonic atoms

A nonrelativistic (NR) theory of recoil corrections to the magnetic moments of bound particles is revisited. A number of contributions can be described within an NR theory with the help of various potentials. We study those potential-type contributions for two-body atomic systems. We have developed an approach, that allows us to find the g factor for an electron or muon in a two-body bound system for an arbitrary electrostatic interaction together with the m/M recoil corrections, as well as the binding corrections to the g factor of the nucleus. We focus our attention on light muonic two-body atoms, where the recoil effects are enhanced. Both mentioned kinds of contributions have been previously known only for the pure Coulomb effects. We have applied the here-obtained master equations to a few particular cases of perturbations of the Coulomb potential. In particular, the results on the recoil corrections to the finite-nuclear-size (FNS) and Uehling-potential contributions to the g factor of the bound muon are obtained. The Uehling-potential and FNS contributions to the g factor of the bound nucleus have been found as well together with the related recoil corrections. We have generalized the results for the case of the g factor of a bound muon in a three-body atomic system consisting of an electron, a muon, and a spinless nucleus.Graphical abstract

Two-dimensional mixture of dipolar fermions: Equation of state and magnetic phases

We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive $1/r^3$ potential. This model can be realized with ultracold atoms or molecules, when their dipole moments are aligned in the confinement direction orthogonal to the plane. We characterize the unpolarized mixture by means of the Diffusion Monte Carlo technique. Computing the equation of state, we identify the regime of validity for a mean-field theory based on a low-density expansion and compare our results with the hard-disk model of repulsive fermions. At high density, we address the possibility of itinerant ferromagnetism, namely whether the ground state can be fully polarized in the fluid phase. Within the fixed-node approximation, we show that the accuracy of Jastrow-Slater trial wave functions, even with the typical two-body backflow correction, is not sufficient to resolve the relevant energy differences. By making use of the iterative-backflow improved trial wave functions, we observe no signature of a fully-polarized ground state up to the freezing density.

L-shell spectroscopy of neon and fluorine like copper ions from laser produced plasma

Ne, F, and O-like Rydberg resonance lines along with some of the inner shell satellite lines of Copper plasma, in the wavelength range of 7.9–9.5 Å, are experimentally observed using a thallium acid phthalate crystal spectrometer. The plasma is produced by the irradiation of a Cu target with a 15 J, 500 ps Nd: Glass laser with a focusable intensity up to 5 × 1014 W/cm2. The observed lines result from the transitions among 2p-nd, 2p-ns, and 2s-nd (n = 4–6) levels. Transition wavelengths, transition probabilities, and oscillator strengths of these lines are calculated using the Multi-Configuration Dirac-Fock method. In this computation, the contribution of relativistic corrections such as two-body Breit corrections and QED corrections due to vacuum polarization and self-energy has also been considered. FLYCHK simulations are used to analyze the distribution of the various charge states of the Copper ions and to find the temperature and density of plasma. Moreover, the effect of self-absorption of the plasma (opacity), as well as of suprathermal electrons on charge state distribution of ions, is also studied. The synthetic spectrum provides a best-match with the experimental spectrum at a laser intensity of 1.3 × 1014 W/cm2 for Tc = 150 eV, Th = 1000 eV, f = 0.008, and density 4.5 × 1020 cm−3.The temperature and density ranges are also calculated using a radiative hydrodynamic code. The calculated temperature and density range are in agreement with the experimentally determined values. The effect of the change in laser intensity on the L-shell spectrum of Cu is studied which indicates the switching between lower (Cu XX) and higher charge states (Cu XXI and Cu XXII) at higher laser intensities.

Vortex formation and vortex lattices in a Bose-Einstein condensate with Lee-Huang-Yang (LHY) correction

We examine the effect of the quantum fluctuation through LHY correction on the vortex formation and the vortex lattices in a rotating Bose-Einstein condensate (BEC) trapped in a harmonic plus quartic potential in detail. To this aim, we numerically solve a quasi-two-dimensional Gross-Pitaevskii equation with two-body interaction and LHY correction and calculate the critical rotation frequency for different possible cases. We show that the LHY correction plays a significant role in determining the critical rotation frequency for vortex formation. We also discuss the impacts of the different strengths of the LHY correction in the vortex formation process. Further, we demonstrate the vortex lattice for a large rotation frequency.

Explicit polarization: a quantum mechanical framework for developing next generation force fields.

ConspectusMolecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantum mechanics rather than only using quantum mechanical results to fit analytic force fields. In this spirit, this approach is called a quantum mechanical force field (QMFF).X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems (“fragments”) to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantum mechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantum mechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples involving water clusters (which show the power of two-body corrections), ethylmethylimidazolium acetate ionic liquids (which reveal that the amount of charge transfer between anion and cation is much smaller than what has been assumed in some classical simulations), and a solvated protein in aqueous solution (which shows that the average charge distribution of carbonyl groups along the polypeptide chain depends strongly on their position in the sequence, whereas they are fixed in most classical force fields). The development of QMFFs also offers an opportunity to extend the accuracy of biochemical simulations to areas where classical force fields are often insufficient, especially in the areas of spectroscopy, reactivity, and enzyme catalysis.

Machine-learning approach for one- and two-body corrections to density functional theory: Applications to molecular and condensed water

We show how machine learning techniques based on Bayesian inference can be used to enhance the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using accurate, correlated quantum chemistry, and predict energies and forces in molecular aggregates ranging from clusters to solid and liquid phases. The widely used electronic-structure methods based on density functional theory (DFT) by themselves give poor accuracy for molecular materials like water, and we show how our techniques can be used to generate systematically improvable one- and two-body corrections to DFT with modest extra resources. The resulting corrected DFT scheme is considerably more accurate than uncorrected DFT for the relative energies of small water clusters and different ice structures and significantly improves the description of the structure and dynamics of liquid water. However, our results for ice structures and the liquid indicate that beyond-two-body DFT errors cannot be ignored, and we suggest how our machine-learning methods can be further developed to correct these errors.

The Miyazawa-Jernigan Contact Energies Revisited

The Miyazawa-Jernigan (MJ) contact potential for globular proteins is a widely used knowledge-based potential. It is well known that MJ’s contact energies mainly come from one-body terms. Directly in the framework of the MJ energy for a protein, we derive the one-body term based on a probabilistic model, and compare the term with several hydrophobicity scales of amino acids. This derivation is based on a set of native structures, and the only information of structures manipulated in the analysis is the contact numbers of each residue. Contact numbers strongly correlate with layers of a protein when it is viewed as an ellipsoid. Using an entropic clustering approach, we obtain two coarse-grained states by maximizing the mutual information between coordination numbers and residue types, and find their differences in the two-body correction. A contact definition using sidechain centers roughly estimated from Cα atoms results in no significant changes.

Improving density functional theory for crystal polymorph energetics

We show that the quality of density functional theory (DFT) predictions for the relative stabilities of polymorphs of crystalline para-diiodobenzene (PDIB) is dramatically improved through a simple two-body correction using wavefunction-based electronic structure theory. PDIB has two stable polymorphs under ambient conditions, and like Hongo et al. [J. Phys. Chem. Lett., 1, 1789 (2010)] we find that DFT makes wildly variable predictions of the relative stabilities, depending on the approximate functional used. The two-body corrected scheme, using Grimme's spin-scaled variant of second-order Møller-Plesset perturbation theory and any of the tested density functionals, predicts the α-polymorph to be more stable, consistent with experiment, and produces a relative stability that agrees with the benchmark quantum Monte-Carlo results of Hongo et al. within statistical uncertainty.

A Technique for Real-Time Shadowing Adjustment of RCS Scattering Center Models

A method has been developed to adjust radar cross section (RCS) scattering models for two-body effects, particularly shadowing. The method described here involves using the near field scattering solution of one object to apply two-body corrections to another. By assuming that the second object can be represented by a known set of point scatterers, the fields at these scattering centers are used to calculate the adjusted RCS in the presence of the shadowing object using the principle of reciprocity. Since this approximation does not require a full-wave electromagnetic solution, it is considerably more computationally efficient than moment method solvers or other similar techniques, and thus could be adapted to real-time applications. The results of the method are compared against measurement and Moment Method simulation for the case of two cylinders, a cylinder and a cone, and two spheres. Good agreement is generally obtained between the proposed approximate model and measurements or Moment Method simulations.

Lamb shift in muonic hydrogen—I. Verification and update of theoretical predictions

In view of the recently observed discrepancy of theory and experiment for muonic hydrogen [R. Pohl et al., Nature 466 (2010) 213], we reexamine the theory on which the quantum electrodynamic (QED) predictions are based. In particular, we update the theory of the 2 P–2 S Lamb shift, by calculating the self-energy of the bound muon in the full Coulomb + vacuum polarization (Uehling) potential. We also investigate the relativistic two-body corrections to the vacuum polarization shift, and we analyze the influence of the shape of the nuclear charge distribution on the proton radius determination. The uncertainty associated with the third Zemach moment 〈 r 3〉 2 in the determination of the proton radius from the measurement is estimated. An updated theoretical prediction for the 2 S–2 P transition is given.

A relativistic approach to the equation of state of asymmetric nuclear matter

The properties of asymmetric nuclear matter for a wide range of densities and asymmetric parameters are investigated within the lowest-order-constrained variational (LOCV) method by employing the relativistic Hamiltonian with a potential which has been fitted relativistically to N-N phase shifts ( $ \tilde{{v}}_{{14}}^{}$ and to the AV14interaction. Like our previous work on symmetric nuclear matter, the boost interaction corrections as well as the relativistic one-body and two-body kinetic corrections are calculated. The various properties of asymmetric nuclear matter such as the symmetry energy, the saturation energy and the validity of the $ \alpha^{2}_{}$ law, etc., are examined. The symmetry energy is reduced by about 7MeV when we use $ \tilde{{v}}_{{14}}^{}$ instead of its non-relativistic version, i.e. the AV14interaction. The results are compared with other many-body calculations.

Covariant spectator theory for the electromagnetic three-nucleon form factors: Complete impulse approximation

We present the first calculations of the electromagnetic form factors of $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$ within the framework of the Covariant Spectator Theory (CST). This first exploratory study concentrates on the sensitivity of the form factors to the strength of the scalar meson-nucleon off-shell coupling, known from previous studies to have a strong influence on the three-body binding energy. Results presented here were obtained using the complete impulse approximation (CIA), which includes contributions of relativistic origin that appear as two-body corrections in a nonrelativistic framework, such as ``Z-graphs,'' but omits other two and three-body currents. We compare our results to nonrelativistic calculations augmented by relativistic corrections of $\mathcal{O}(v/c){}^{2}$.

Wavefunction and energy of the 1s22sns configuration in a beryllium atom

A new set of trial functions for 1s22sns configurations in a beryllium atom is suggested. A Mathematica program based on the variational method is developed to calculate the wavefunctions and energies of 1s22sns (n = 3–6) configurations in a beryllium atom. Non-relativistic energy, polarization correction and relativistic correction which include mass correction, one-and two-body Darwin corrections, spin-spin contact interaction and orbit-orbit interaction, are calculated respectively. The results are in good agreement with experimental data.

Nuclear structure and reactions in the fermionic molecular dynamics approach

The Fermionic Molecular Dynamics (FMD) model uses Gaussian wave packets as single-particle states. Intrinsic many-body basis states are constructed as Slater determinants which have to be projected on parity, angular momentum and total linear momentum to restore the symmetries of the Hamiltonian. The flexibility of the Gaussian basis allows to economically describe states with shell structures as well as states featuring clustering or halos. We use an effective interaction that is derived from the realistic Argonne V18 interaction by means of the Unitary Correlation Operator Method (UCOM). A phenomenological momentum-dependent two-body correction simulates contributions from missing three-body forces and three-body correlations. We discuss 12C with a special emphasis on the structure of the excited 0+ and 2+ states. We analyze the degree of α-clustering and confirm, taking inelastic electron scattering data into account, the conjecture that the Hoyle state has to be understood as a loosely bound system of alpha particles. We will also present first results on the application of FMD for the calculation of scattering phase shifts in 3He — 4He.

Extended Hartree-Fock method based on pair density functional theory

A practical electronic structure method in which a two-body functional is the fundamental variable is constructed. The basic formalism of our method is equivalent to Hartree-Fock density matrix functional theory [M. Levy, in Density Matrices and Density Functionals, edited by R. Erdahl and V. H. Smith, Jr. (Reidel, Dordrecht, 1987)]. The implementation of the method consists of solving Hartree-Fock equations and using the resulting orbitals to calculate two-body corrections to account for correlation. The correction terms are constructed so that the energy of the system in the absence of external potentials can be made to correspond to approximate expressions for the energy of the homogeneous electron gas. In this work, the approximate expressions we use are based on the high-density limit of the homogeneous electron gas. Self-interaction is excluded from the two-body functional itself. It is shown that our pair density based functional does not suffer from the divergence present in many density functionals when homogeneous scaling is applied. Calculations based on our pair density functional lead to quantitative results for the correlation energies of atomic test cases.

General calculation of 4f-5d transition rates for rare-earth ions using many-body perturbation theory

The 4f-5d transition rates for rare-earth ions in crystals can be calculated with an effective transition operator acting between model 4f(N) and 4f(N-1)5d states calculated with effective Hamiltonian, such as semiempirical crystal Hamiltonian. The difference of the effective transition operator from the original transition operator is the corrections due to mixing in transition initial and final states of excited configurations from both the center ion and the ligand ions. These corrections are calculated using many-body perturbation theory. For free ions, there are important one-body and two-body corrections. The one-body correction is proportional to the original electric dipole operator with magnitude of approximately 40% of the uncorrected electric dipole moment. Its effect is equivalent to scaling down the radial integral (5d/r/4f) to about 60% of the uncorrected HF value. The two-body correction has magnitude of approximately 25% relative to the uncorrected electric dipole moment. For ions in crystals, there is an additional one-body correction due to ligand polarization, whose magnitude is shown to be about 10% of the uncorrected electric dipole moment.

Coulomb exchange and pairing contributions in nuclear Hartree–Fock–Bogoliubov calculations with the Gogny force

We present exact Hartree–Fock–Bogoliubov calculations with the finite-range density-dependent Gogny force using a triaxial basis. For the first time, all contributions to the pairing and Fock fields arising from the Gogny and Coulomb interactions as well as the two-body correction of the kinetic energy have been calculated in this basis. We analyze the relevance of these terms in different regions of the periodic table at zero and high angular momentum. The validity of commonly used approximations that neglect different terms in the variational equations is also checked. We find a decrease of the proton-pairing energies mainly due to a Coulomb antipairing effect.

Quantum chemical study of neutral and single charged palladium clusters

The extended Hückel (EH) method with an electrostatic two-body correction, has been used in order to determine the structures of small single charged Pd n clusters with n=2–13 and to compare them with the neutral ones. The results for Pd 2 and Pd 3 are compared with density functional (DFT) calculations. Both cation and anion formations were found to strengthen the clusters due to the bonding character of their HOMO and antibonding nature of LUMO. The twin formation with bond lengths significantly smaller than those in the bulk palladium and in the corresponding neutral particles was found to be the preferential way of growth for anionic clusters; cationic clusters show a more complicated behavior. The promotion of occupation of Pd 5 s AOs is suggested to be responsible for the formation of 3D structures, whereas the stability of the planar configurations is attributed to the appearance of the vacancy in the valence 4 d-shell. As a result of stronger intermetallic interaction in charged clusters, both excess and deficit of electron density were found to cause the significant broadness of the d-zone.