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We investigate pfaffian trial wave functions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians. Following upon our previous study \cite{pfaffianprl}, we explore the possibilities of expanding the wave function in linear combinations of pfaffians. We observe that molecular systems require much larger expansions than atomic systems and linear combinations of a few pfaffians lead to rather small gains in correlation energy. We also test the wave function based on fully-antisymmetrized product of independent pair orbitals. Despite its seemingly large variational potential, we do not observe additional gains in correlation energy. We find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions and exhibit the minimal number of two nodal domains in agreement with recent results on fermion nodes topology. We analyze the nodal structure differences of Hartree-Fock, pfaffian and essentially exact large-scale configuration interaction wave functions. Finally, we combine the recently proposed form of backflow correlations \cite{drummond_bf,rios_bf} with both determinantal and pfaffian based wave functions., 13 pages, 4 tables, 3 figure, submitted to PRB

One-dimensional models of quantum many-body systems have received a great deal of a t tent ion over the years, 1 not only because they are more mathematically t ractable,2 but also because they are experimental ly accessible. Among the most popular theoret ical models of quasi-one-dimensional are the Hubbard 3 Hamiltonians. These have served as models for the study of organic conductors as well as the invest igat ion of sol i tons in materials l i ke polyacetylene. In i t s simplest form the Hamiltonian

The $^{1}S_{0}$ pairing in neutron matter is studied using realistic two- and three-nucleon interactions. The auxiliary field diffusion Monte Carlo method and correlated basis function theory are employed to get quantitative and reliable estimates of the gap. The two methods are in good agreement up to the maximum gap density and both point to a slight reduction with respect to the standard BCS value. In fact, the maximum gap is about 2.5 MeV at ${k}_{F}\ensuremath{\sim}0.8\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}1}$ in BCS and 2.2--2.4 MeV at ${k}_{F}\ensuremath{\sim}0.6\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}1}$ in correlated matter. In general, the computed medium polarization effects are much smaller than those previously estimated within all theories. Truncations of Argonne ${v}_{{8}^{\ensuremath{'}}}$ to simpler forms give the same gaps in BCS, provided the truncated potentials have been refitted to the same $NN$ data set. The three-nucleon interaction provides an additional increase of the gap of about 0.35 MeV.

We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the s-wave scattering length and the Fermi wave vector, $ak_F$. We report results for the ground state energy, the pairing gap $��$ and the quasiparticle spectrum. In the weak coupling regime, $1/ak_F < -1$, we obtain BCS superfluid and the energy gap $��$ is much smaller than the Fermi gas energy $E_{FG}$. When $ a > 0$, the interaction is strong enough to form bound molecules with energy $E_{mol}$. For $1/ak_F \gtrsim 0.5$ we find that weakly interacting composite bosons are formed in the superfluid gas with $��$ and gas energy per particle approaching $|E_{mol}|/2$. In this region we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS to BEC transition region, $-0.5 < 1/ak_F < 0.5$ is discussed., 11 figures, 3 tables

Iron grown on room‐temperature CaF2/Si(111) substrates form two‐dimensional arrays of nanometer‐sized superparamagnetic islands. Deposition of Ag on the Fe/CaF2/Si(111) produced a superparamagnetic response where the effective moment was proportional to the number of Fe islands covered by an average‐sized Ag island. The nonmagnetic Ag overlayer mediates a long‐range exchange between neighboring Fe islands within an individual Ag island. Monte Carlo methods are used to examine ordering in two dimensions and to set minimum interisland coupling strengths.

We report quantum Monte Carlo calculations of superfluid Fermi gases with short-range two-body attractive interactions with infinite scattering length. The energy of such gases is estimated to be $(0.44 \pm 0.01)$ times that of the noninteracting gas, and their pairing gap is approximately twice the energy per particle., Comment: 4 pages, 4 figures

Quantum 5D bound state calculations for the fully solvated Ar12HF cluster, with the Ar atoms frozen at their icosahedral equilibrium geometry, gave the HF vibrational redshift of 42.46 cm−1. This value is equal to that measured for HF in an Ar matrix, 42.4 cm−1.

We present diffusion quantum Monte Carlo calculations of the interchange tunneling splitting of (4)He(n)(HF)(2) clusters, n = 1-10. The tunneling splitting decreases rapidly for n = 1-4 clusters, and much more slowly for n>4. The decrease calculated for (4)He(n)(HF)(2) represents 74% of the reduction in the tunneling splitting measured recently for HF dimer in nanodroplets of more than 2000 He atoms. The first four He atoms quench the interchange tunneling very efficiently by virtue of occupying the equatorial ring which encircles the C(2h) transition state of the tunneling pathway.

We present a general formulation of the Green's function Monte Carlo method in imaginary-time quantum Monte Carlo which employs exact propagators. This algorithm has no time-step errors and is obtained by minimal modifications of the time-independent Green's function Monte Carlo method. We describe how the method can be applied to the many-body Schr\"odinger equation, lattice Hamiltonians, and simple field theories. Our modification of the Green's function Monte Carlo algorithm is applied to the ground state of liquid ${}^{4}\mathrm{He}.$ We calculate the zero-temperature imaginary-time diffusion constant and relate that to the effective mass of a mass-four ``impurity'' atom in liquid ${}^{4}\mathrm{He}.$

The auxiliary field diffusion Monte Carlo method is applied to compute the spin susceptibility and the compressibility of neutron matter at zero temperature. Results are given for realistic interactions which include both a two-body potential of the Argonne type and the Urbana IX three-body potential. Simulations have been carried out for about 60 neutrons. We find an overall reduction of the spin susceptibility by about a factor of 3 with respect to the Pauli susceptibility for a wide range of densities. Results for the compressibility of neutron matter are also presented and compared with other available estimates obtained for semirealistic nucleon-nucleon interactions by using other techniques.

We use a local-orbital formalism based on density-functional theory to investigate the stoichiometry and structure of the cation- and anion-terminated (0001) surfaces of wurtzite-phase GaN and A1N. We compare the total energies computed for various p(2×2) reconstructions. First-layer atom deficient structures such as vacancies are found to be the most stable configurations for the anion- and cation-terminated surfaces. For metal rich growth conditions our calculations favor the adsorption of metal atoms. Surface chemical reactions relevant for the growth of thin nitride films, such as the adsorption of hydrogen and nitrogen from decomposed ammonia, are discussed. We determine the total energy differences for the co-adsorption of NH2 and H on different surface structures.

Background An 18 year old female with history of myelomeningocele and hydrocephalus had her ventriculoperitoneal shunt converted to a VA shunt following development of peritonitis at age 11 years. Seven years later she was admitted with abdominal pain. CT revealed a perihepatic abscess and incidental right lower lobe pulmonary embolus (PE). Further investigation revealed a large right cardiac ventricle thrombus. She underwent open thrombectomy and was anticoagulated. Pathologic evaluation of the thrombus demonstrated focal purulent inflammation without identifiable organisms.

X-ray diffraction patterns may be obtained from individual submicron protein nanocrystals using a femtosecond pulse from a free-electron X-ray laser. Many "single-shot" patterns are read out every second from a stream of nanocrystals lying in random orientations. The short pulse terminates before significant atomic (or electronic) motion commences, minimizing radiation damage. Simulated patterns for Photosystem I nanocrystals are used to develop a method for recovering structure factors from tens of thousands of snapshot patterns from nanocrystals varying in size, shape and orientation. We determine the number of shots needed for a required accuracy in structure factor measurement and resolution, and investigate the convergence of our Monte-Carlo integration method.

Previous theoretical studies and molecular-dynamics simulations show that a periodic one-dimensional lattice with nearest-neighbor quadratic and quartic interactions supports stationary localized modes. The most localized of these are an odd-parity mode with a displacement pattern A(. . . ,0,-1/2,1,-1/2,0, . . .) and an even-parity mode A(. . . ,0,-1,1,0. . .), where A is the amplitude. These solutions are asymptotically exact for the pure even-order anharmonic lattice in the limit of increasing order. We show here that in both this asymptotic limit and for the harmonic plus quartic lattice, the odd-parity mode is unstable to infinitesimal perturbations, while the even-parity mode is stable. For the pure quartic case, the predicted growth rate for the instability is 0.15 in units of the mode frequency, in excellent agreement with the rate observed in our molecular-dynamics simulations. In contrast, we observe the even-parity mode to persist unchanged over more than 32 000 mode oscillations. Our simulations show that the instability does not destroy the odd mode, but causes it to move. We will also discuss a smoothly traveling version of these modes. As they move, these modes have a nonconstant phase difference between adjacent relative displacements, in contrast with traveling modes discussed previously by others.

We describe a basis set approach to optimize quantum fluid and solid wave functions. We test the method on 4He using the hypernetted chain approximation and compare to paired-phonon analysis results. We show that only about ten variational parameters are needed to accurately specify an optimized Jastrow correlation. We then give some preliminary results using Monte Carlo integration to optimize these parameters for both the liquid and the solid.

We consider a monodispersed Rayleigh droplet beam of water droplets doped with proteins. An intense infrared laser is used to align these droplets. The arrangement has been proposed for electron- and x-ray-diffraction studies of proteins which are difficult to crystallize. This paper considers the effect of thermal fluctuations on the angular spread of alignment in thermal equilibrium, and relaxation phenomena, particularly the damping of oscillations excited as the molecules enter the field. The possibility of adiabatic alignment is also considered. We find that damping times in a high-pressure gas cell as used in x-ray-diffraction experiments are short compared with the time taken for molecules to traverse the beam and that a suitably shaped field might be used for electron-diffraction experiments in vacuum to provide adiabatic alignment, thus obviating the need for a damping gas cell.

The effective magnetic moment was measured as a function of Fe island size during the initial stages of Fe growth on CaF2/Si(111) in an ultrahigh vacuum scanning electron microscope equipped with an in situ SMOKE analysis chamber. This substrate was selected for its wide bandgap, chemical inertness, viability of integration into an Si based technology and the availability of nanopatterning using electron beams for producing devices. Fe grown at room temperature initially nucleates into a monodisperse distribution of 3‐D islands at very high nucleation densities (8×1012/cm2). Increased Fe coverages lead to 2‐D island growth. A room temperature superparamagnetic to ferromagnetic phase transition occurs as a function of Fe island radius. Mean field and Monte Carlo calculations illustrate that three distinct magnetic phases exist as a function of island diameter. Ferromagnetic order is present at room temperature when r≳3 nm, superparamagnetism is favored when 2 nm < r

The Green's function Monte Carlo method, which yields an exact ground-state solution to the Schroedinger equation for Bose systems, is applied to liquid /sup 3/He, a fermion system. With use of a technique that projects out states of selected symmetry, strict upper bounds to the ground-state energy of many-fermion systems are constructed. It is found that such an upper bound for liquid /sup 3/He of -2.20 +- 0.05 /sup 0/K at the experimental equilibrium density. This energy is more than 1 /sup 0/K below Jastrow variational results, and much nearer the experimental value of -2.47 +- 0.01 /sup 0/K.

A Monte Carlo method for obtaining exact ground-state properties of a class of Hubbard Hamiltonians is described. Results are presented for two special cases, nearest-neighbor Coulomb and on-site interactions, where previous exact results are known. The straightforward applicability of the method to a wider variety of interactions is demonstrated.

The first Monte Carlo calculations explicitly employing triplet correlations in the variational wave function for the ground state of $^{4}\mathrm{He}$ are presented. A significant lowering of energy is obtained, accounting for 75% of the discrepancy between previous Jastrow variational calculations and the known exact numerical results. An improved density dependence of the energy is obtained and the pair correlation function is sharpened leading to much better agreement with the exact ground state.

The variational and Green's function Monte Carlo (GFMC) methods can treat many interesting atomic and molecular problems. These methods can give chemical accuracy for up to 10 or so electrons. The various implementations of the GFMC method, including the domain Green's function method and the short-time approximation, are discussed. Results are presented for several representative atoms and molecules.

The results of applying the simulated annealing method to find the lowest energy structure of the decane molecule are analyzed. The algorithm is found to be both efficient and economical. Some preliminary results are presented for a molecule of biochemical interest, Met-enkephalin.

Using a potential model, constrained by the hadron spectrum, for the confinement of relativistic quarks we explore the consequences of the substructure of nucleons for the binding energy and ground state wavefunction of 4 He. In its simplest form, this model gives a binding energy of 19 MeV. Quark wavefunctions differ from those associated with free nucleons by less than 10%, the rms quark radius is 1.34 fm and the resulting structure differs considerably from that of an expansion beginning from the (0s) 4 shell model. Considerable contributions to the binding energy, attractive from quark delocalization and repulsive from the quark hyperfine interaction, appear unavoidable. We conclude that these effects cannot be excluded from a detailed understanding of the properties of nuclear ground states.

Approximate wave functions of the form $\mathcal{G}\ensuremath{\Phi}(n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}))$, where $\mathcal{G}$ is a correlation operator that contains two-body, three-body, and momentum-dependent correlations, and $\ensuremath{\Phi}(n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}))$ is a noninteracting-Bose-gas wave function with occupation numbers $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$, are used to calculate the energies of excited states of liquid $^{4}\mathrm{He}$. The energy expectation values are calculated by generalizing the Fermi hypernetted-chain methods. The single-quasiparticle excitation spectrum provides stringent tests for the correlation operator $\mathcal{G}$. The calculated phonon, maxon spectra are not in good agreement with the experimental results presumably because of the truncations in the large-distance behavior of the two-body correlations in the $\mathcal{G}$. The results obtained for the roton energies are in good agreement with the experiments over the range of liquid-$^{4}\mathrm{He}$ density.

We review variational calculations with a Jastrow wave function and show they are inadequate to calculate the zero-temperature equation of state E ( ρ ) for liquid helium. The importance of the Feynman-Cohen backflow around a moving particle is then discussed, and a variational wave function incorporating backflow is proposed. Results with this wave function are discussed for 3 He, 4 He and the v 2 potential model of nuclear matter. In both 4 He and 3 He the new wave function gives an energy and equilibrium density much closer to the experimental values than the Jastrow form. In the v 2 model the addition of the backflow terms to the Jastrow correlation lowers the energy by 2–3 MeV. Spin-isospin correlations can simulate the state dependence of the backflow correlation at small momenta. However, at nuclear-matter densities they can produce only about half of the lowering due to backflow.

The Green’s function Monte Carlo method used for obtaining exact solutions to the Schrodinger equation of boson systems is generalized to treat systems of several fermions. We show that when it is possible to select eigenfunctions of the Hamiltonian based on physical symmetries, the GFMC method can be used to yield the lowest energy state of that symmetry. In particular, the lowest totally antisymmetric eigenfunction, the fermion ground state, can be obtained. Calculations on several two‐ and three‐body model problems show the method to be computationally feasible for few‐body systems.

Renormalization-group methods are used to produce a novel Monte Carlo sampling algorithm which alleviates the problem of critical slowing down. The method is applied by means of a Kadanoff block-spin transformation to the one- and two-dimensional Ising models.

A model Hamiltonian, designed to allow larger systems to be treated with the Green’s function Monte Carlo method, is introduced for atomic and molecular systems. The model reduces the statistical variance associated with Green’s function Monte Carlo calculations by reducing potential energy fluctuations in the core regions. By performing calculations of Li, LiH, and Li2 we show that this method can be used to obtain energy differences with much less computer time than required for the complete interaction. Increases in efficiency for larger systems will be even greater.

We present a new Green’s function Monte Carlo method for solving for the ground state of the Schrodinger equation. Unlike the commonly used short time approximation this method has no time step error. We formulate the method so that the attractive Coulomb singularities are isolated and can be accurately sampled. The algorithm is used to obtain the ground state energies of the following atomic systems: H, He and the helium‐like ions of Be, N, and O. The results compare favorably with the experimental ground state energies.

The behavior of the specific heat of liquid /sup 3/He, over a wide range of temperature, indicates a wiggle in the single- (quasi-) particle spectrum e(k) at k/sub F/. This wiggle corresponds to the enhancement of the effective mass m*(k) at k/sub F/ of current interest in nuclear physics. It can be quantitatively understood from the microscopic Hamiltonian within correlated basis perturbation theory.

Variational methods developed for the ground-state are extended to the calculation of the finite temperature properties of nuclear matter. Results for the effective mass and free energy are given, and the behavior of m ∗ (ϱ, T) is compared with the predictions of Skryme models.

Variational calculations, with a new wave function based on the Feynman-Cohen correlation operator, are carried out for liquid $^{3}\mathrm{He}$ with a Lennard-Jones potential. The wave function contains three-body correlations and momentum-dependent two-body correlations, in addition to the Jastrow correlations commonly used in variational calculations. The Fermi hypernetted-chain summation methods are generalized to calculate energy expectation values wiith this wave function. The calculated equilibrium energy and density are -2.\ifmmode\pm\else\textpm\fi{}0.1 \ifmmode^\circ\else\textdegree\fi{}K and $0.28\ifmmode\pm\else\textpm\fi{}0.01{\ensuremath{\sigma}}^{\ensuremath{-}3}$, a significant improvement over the -1.25\ifmmode^\circ\else\textdegree\fi{}K and $0.22{\ensuremath{\sigma}}^{\ensuremath{-}3}$ obtained with the Jastrow wave function, and closer to the experimental -2.56\ifmmode^\circ\else\textdegree\fi{}K and $0.28{\ensuremath{\sigma}}^{\ensuremath{-}3}$.

Using the Metropolis Monte Carlo integration technique, we calculate upper bounds to the correlation energy of a Be atom for a variety of wave functions. With this method, it is simple to treat unconventional wave functions, including those which depend on the interelectronic distance rij. We obtain about 40% of the correlation energy by using only a simple two‐parameter Jastrow function of rij with a single Slater determinant of Hartree–Fock orbitals. A four configuration wave function with this Jastrow function yields 87% of the correlation energy. Several wave functions derived from nonvariational methods are shown to give no correlation energy when used in a strictly variational computation.

A new computational method for the location of the lowest energy conformation of flexible molecules is reported. The technique, called simulated annealing, is discussed and several applications are described.

The potential energy surface of the LiH molecule is calculated using the Green’s function Monte Carlo method. The calculated correlation energy is 0.078±0.001 hartree and the binding energy is 2.56 eV. These results are within 6% and 2% of the experimental values, respectively. The Green’s function Monte Carlo method is discussed in some detail with particular emphasis on problems of chemical interest.

Microscopic calculations of low energy alpha neutron scattering are reported for the resonant J/sup ..pi../ = (1/2/sup -/ and (3/2/sup -/ states. A good qualitative fit to the experimental LxS splitting is obtained, although discrepancies of the order of 1--2 MeV remain. Results with two different nucleon-nucleon interaction models are presented, and the effects of three-nucleon interactions are discussed.

An implementation of the domain Green’s function Monte Carlo algorithm is described. Unlike the short time approximation, the method is variational and exact within the limits of the fixed node approximation. The systems investigated include LiH, Be in the ground and first excited states, a study of the C2v insertion pathway of Be into H2, and H2O. We predict a barrier of 0.190 hartree for the insertion reaction with a statistical accuracy of ±2%. Better than 90% of the correlation energy is recovered in each case, which makes these some of the most accurate computations to date.