Jacob's Ladder Research Articles

Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy.

From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully nonlocal. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard density functional theory (DFT) functionals, are captured by the highly nonlocal structure, which goes beyond the “Jacob’s ladder” framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.

Performance of wave function and density functional methods for water hydrogen bond spin-spin coupling constants.

Spin-spin coupling constants in water monomer and dimer have been calculated using several wave function and density functional-based methods. CCSD, MCSCF, and SOPPA wave functions methods yield similar results, specially when an additive approach is used with the MCSCF. Several functionals have been used to analyze their performance with the Jacob's ladder and a set of functionals with different HF exchange were tested. Functionals with large HF exchange appropriately predict 1 J O H , 2 J H H and 2h J O O couplings, while 1h J O H is better calculated with functionals that include a reduced fraction of HF exchange. Accurate functionals for 1 J O H and 2 J H H have been tested in a tetramer water model. The hydrogen bond effects on these intramolecular couplings are additive when they are calculated by SOPPA(CCSD) wave function and DFT methods. Graphical Abstract Evaluation of the additive effect of the hydrogen bond on spin-spin coupling constants of water using WF and DFT methods.

An assessment of the random-phase approximation functional and characteristics analysis for noncovalent cation-π interactions.

The binding energy is of great importance in understanding the formation and stability of noncovalent interactions. However, the determination of the binding energy with high precision and efficiency in medium- and long-range noncovalent interactions is still challenging for quantum chemistry. Here, we assess the performance of random-phase approximation (RPA), a fully non-local fifth-rung of the Jacob ladder functional, in determining the binding energy of cation-π systems (cation = Li+, Na+, Be2+, Mg2+, Al+, and NH4+; π = C6H6), which, to the best of our knowledge, has not been investigated. Using experimental results as the benchmark, we systematically compared the RPA method to the other ab initio methods (DFT/B3LYP, MP2, CCSD(T), and QCISD(T)) both in calculation accuracy and efficiency. From the perspective of accuracy, RPA is the best among these approaches, followed by the CCSD(T) and QCISD(T) methods. DFT/B3LYP and MP2 provide the worst accuracy. In addition, the computational efficiency of RPA is much faster than that of CCSD(T) and QCISD(T). We believe that RPA is a robust method for the precise description of medium- and long-range noncovalent interactions and is capable of providing benchmarking data. The interaction strength and interaction nature of cation-π systems are further analyzed by atoms in molecules (AIM) and the color-mapped reduced density gradient (RDG) isosurface, which are consistent with the characteristics of a typical cation-π interaction.

How reliable is DFT in predicting relative energies of polycyclic aromatic hydrocarbon isomers? comparison of functionals from different rungs of jacob's ladder.

Density functional theory (DFT) is the only quantum-chemical avenue for calculating thermochemical/kinetic properties of large polycyclic aromatic hydrocarbons (PAHs) such as graphene nanoflakes. Using CCSD(T)/CBS PAH isomerization energies, we find that all generalized gradient approximation (GGA) and meta GGA DFT functionals have severe difficulties in describing isomerization energies in PAHs. The poor performance of these functionals is demonstrated by the following root-mean-square deviations (RMSDs) obtained for a database of C14 H10 and C18 H12 isomerization energies. The RMSDs for the GGAs range between 6.0 (BP86-D3) and 23.0 (SOGGA11) and for the meta GGAs they range between 3.5 (MN12-L) and 11.9 (τ-HCTH) kJmol-1 . These functionals (including the dispersion-corrected methods) systematically and significantly underestimate the isomerization energies. A consequence of this behavior is that they all predict that chrysene (rather than triphenylene) is the most stable C18 H12 isomer. A general improvement in performance is observed along the rungs of Jacob's Ladder; however, only a handful of functionals from rung four give good performance for PAH isomerization energies. These include functionals with high percentages (40-50%) of exact Hartree-Fock exchange such as the hybrid GGA SOGGA11-X (RMSD = 1.7 kJmol-1 ) and the hybrid-meta GGA BMK (RMSD = 1.3 kJmol-1 ). Alternatively, the inclusion of lower percentages (20-30%) of exact exchange in conjunction with an empirical dispersion correction results in good performance. For example, the hybrid GGA PBE0-D3 attains an RMSD of 1.5 kJmol-1 , and the hybrid-meta GGAs PW6B95-D3 and B1B95-D3 result in RMSDs below 1 kJmol-1 . © 2016 Wiley Periodicals, Inc.

The Lost Tycoon: Allan Dwan in the Works of F. Scott Fitzgerald

Abstract F. Scott Fitzgerald identified Allan Dwan's parties as a source for chapter 3 of The Great Gatsby, but who was Dwan and how did he influence Fitzgerald's work? An inventive and prolific director, Allan Dwan (1885–1981) was one of the most successful filmmakers of the silent era, combining the skills of an engineer, an artist, and a businessman. Fitzgerald met him in 1923, during a visit to the set of Dwan's movie The Glimpses of the Moon. That summer, he went to Dwan's parties, mingling with Gloria Swanson and the movie crowd, while Dwan accompanied the Fitzgeralds to the opening night of Fitzgerald's play, The Vegetable. By the end of 1924, however, the two parted ways. The reasons why are unclear. Nonetheless, Fitzgerald drew upon Dwan more frequently for his fiction than any other director, in part as the quintessence of all he found gorgeously wrong with Hollywood, in part as a secret double for himself. Dwan was Lois Moran's close friend at the time Fitzgerald met her, and Dwan left his imprint not only on The Great Gatsby but also on “Jacob's Ladder,” “Magnetism,” “Crazy Sunday,” Tender Is the Night, “Two Old Timers,” and possibly The Love of the Last Tycoon.

The Lost Tycoon: Allan Dwan in the Works of F. Scott Fitzgerald

Abstract F. Scott Fitzgerald identified Allan Dwan's parties as a source for chapter 3 of The Great Gatsby, but who was Dwan and how did he influence Fitzgerald's work? An inventive and prolific director, Allan Dwan (1885–1981) was one of the most successful filmmakers of the silent era, combining the skills of an engineer, an artist, and a businessman. Fitzgerald met him in 1923, during a visit to the set of Dwan's movie The Glimpses of the Moon. That summer, he went to Dwan's parties, mingling with Gloria Swanson and the movie crowd, while Dwan accompanied the Fitzgeralds to the opening night of Fitzgerald's play, The Vegetable. By the end of 1924, however, the two parted ways. The reasons why are unclear. Nonetheless, Fitzgerald drew upon Dwan more frequently for his fiction than any other director, in part as the quintessence of all he found gorgeously wrong with Hollywood, in part as a secret double for himself. Dwan was Lois Moran's close friend at the time Fitzgerald met her, and Dwan left his imprint not only on The Great Gatsby but also on “Jacob's Ladder,” “Magnetism,” “Crazy Sunday,” Tender Is the Night, “Two Old Timers,” and possibly The Love of the Last Tycoon.

Hartree potential dependent exchange functional.

We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e., the electron density, its gradient, and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for the exchange of any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob's ladder classification of non-empirical density functionals.

Exchange-Correlation Catastrophe in Cu-Au: A Challenge for Semilocal Density Functional Approximations.

Semilocal density functional approximations occupy the second rung of the Jacob's ladder model and are thus expected to have certain limits to their applicability. A recent study [Y. Zhang, G. Kresse, and C. Wolverton, Phys. Rev. Lett. 112, 075502 (2014)] hypothesizes that the formation energy, being one of the key quantities in alloy theory, would be beyond the grasp of semilocal density functional theory (DFT). Here, we explore the physics of semilocal DFT formation energies and shed light on the connection between the accuracy of the formation energy and the ability of a semilocal approximation to produce accurate lattice constants. We demonstrate that semilocal functionals designed to perform well for alloy constituents can concomitantly solve the problem of alloy formation energies.

Between the Creator and the Crucified - Understanding of Christian Faith through Anglo-Catholic Theologian, Austin Farrer -

Austin Farrer was possibly the greatest Anglican mind of the twentieth century. Many Western scholars and preachers would agree with this statement, describing him as “the greatest Anglican thinker of his generation.” Susan Howatch, an editor of a collection lf Farrer’s lectures, tries to explain him as “a Prayer-Book Anglican in the Tractarian tradition” and “quintessential Anglican Catholic.” Actually, He led the Anglo-Catholic wing of the Church of England in the mid-twentieth century. However, Austin Farrer is not still an well-known figure in Korean Christian scholars and preachers. If so, why do we, Korean Christians, give our interest on him? To study him gives some benefits. For a start, this research can explore what the Anglican spirituality is. In the course of wrestling with it, we can see another way to understand christian faith, even though our religious traditions are not much similar with the Church of England. More importantly, Farrer’s theological and practical understanding of faith helps our struggle examine the tension between faith and reason or spirituality and philosophy founded around Christian's lives. The most important contribution of Farrer is that he shows us how the unity of them can be established in his understanding of God. His notion of ‘double agency’ which is used to be expressed in ‘Jacob’s laddar’ is Farrer’s predominant contribution to Christian thought. Simply speaching, his ‘double agency’ means that human actions are fully our own but also are the work of God, though perfectly hidden. For him, an entire faith is balanced by a luminous philosophical wisdom. Farrer's image of Jacob's ladder for this two-way relationship between the finite and the Infinite helps us to travel in the unity of theology and spirituality.

The XYG3 type of doubly hybrid density functionals

Doubly hybrid (DH) functionals have emerged as a new class of density functional approximations (DFAs), which not only have a nonlocal orbital‐dependent component in the exchange part, but also incorporate the information of unoccupied orbitals in the correlation part, being at the top rung of Perdew's view of Jacob's ladder in DFAs. This review article focuses on the XYG3 type of DH (xDH) functionals, which use a low rung functional to perform the self‐consistent‐field calculation to generate orbitals and densities, with which a top rung DH functional is used for final energy evaluation. We will discuss the theoretical background of the xDH functionals, briefly reviewing the adiabatic connection formalism, coordinate scaling relations, and Görling–Levy perturbation theory. General performance of the xDH functionals will be presented for both energies and structures. In particular, we will present the fractional charge behaviors of the xDH functionals, examining the self‐interaction errors, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps. This provides a theoretical rationale for the observed good performance of the xDH functionals. WIREs Comput Mol Sci 2016, 6:721–747. doi: 10.1002/wcms.1274This article is categorized under: Electronic Structure Theory > Density Functional Theory

Rungs 1 to 4 of DFT Jacob's ladder: Extensive test on the lattice constant, bulk modulus, and cohesive energy of solids.

A large panel of old and recently proposed exchange-correlation functionals belonging to rungs 1 to 4 of Jacob's ladder of density functional theory are tested (with and without a dispersion correction term) for the calculation of the lattice constant, bulk modulus, and cohesive energy of solids. Particular attention will be paid to the functionals MGGA_MS2 [J. Sun et al., J. Chem. Phys. 138, 044113 (2013)], mBEEF [J. Wellendorff et al., J. Chem. Phys. 140, 144107 (2014)], and SCAN [J. Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] which are meta-generalized gradient approximations (meta-GGA) and are developed with the goal to be universally good. Another goal is also to determine for which semilocal functionals and groups of solids it is beneficial (or not necessary) to use the Hartree-Fock exchange or a dispersion correction term. It is concluded that for strongly bound solids, functionals of the GGA, i.e., rung 2 of Jacob's ladder, are as accurate as the more sophisticated functionals of the higher rungs, while it is necessary to use dispersion corrected functionals in order to expect at least meaningful results for weakly bound solids. If results for finite systems are also considered, then the meta-GGA functionals are overall clearly superior to the GGA functionals.

Isotropic polarizability of ozone from double-hybrid approximations

Literature survey on the electric response properties of ozone reveals that the accurate prediction of its dipole polarizability and resolving the discrepancies in this context is a challenging case to current structure theories. In this Letter, we report the results of approximations from the highest rung of Jacob's ladder, double-hybrid (DH) functionals, for dipole polarizability of ozone. Benchmarking the two families of DHs, parameterized and parameter-free models, we find that the functionals B2Ͽ-PLYP and PBE0-DH as empirical and nonempirical DHs, respectively, provide the results in line with those obtained from the high correlated ab initio approaches.

Jacob's ladder of approximations to paraxial dynamic electron scattering

Dynamical scattering theory describes the dominant scattering process of beam electrons at targets in the transmission electron microscope (TEM). Hence, practically every quantitative TEM study has to consider its ramifications, typically by some approximate modeling. Here, we elaborate on a hierarchy within the various approximations focusing on the two principal approaches used in practice, Bloch wave and multislice. We reveal characteristic differences in the capability of these methods to reproduce the correct local propagation of the wave function, while convergent results are obtained over larger propagation distances. We investigate the dependency of local variations of the wave function on the atomic number of the atomic scatterers and discuss their significance for, e.g., inelastic scattering.

Rare Plants of Canaan Valley, West Virginia

Abstract Canaan Valley (hereafter, the Valley), in northeastern West Virginia, supports large areas of wetland, upland forest, and upland non-forest habitats at relatively high elevations, providing potential habitat for a variety of rare plant species. The presence of 54 species of plants considered to be rare and of conservation concern in West Virginia plus 22 watchlist species has been confirmed in the Valley. No federally listed threatened or endangered plants have been found. One of the rare species is the globally critically imperiled Platanthera shriveri (Shriver's Frilly Orchid) and 4 are globally vulnerable—Gymnocarpium appalachianum (Appalachian Oak Fern), Hypericum mitchellianum (Blue Ridge St. Johnswort), Euphorbia purpurea (Glade Spurge), and Polemonium vanbruntiae (Bog Jacob's-ladder). Rare plants are found throughout the Valley; 80% occur in wetlands, and a significant assemblage is associated with wetlands on Greenbrier Limestone. Globally rare species are Appalachian endemics, but 41 of ...

Curved-folding-inspired deployable compliant rolling-contact element (D-CORE)

This work describes a deployable compliant rolling-contact element joint (D-CORE joint) that employs curved-folding origami techniques to enable transition from a flat to deployed state. These deployable joints can be manufactured from a single sheet of material. Two fundamental configurations of the D-CORE are presented. The first configuration allows for motion similar to that of a Jacob's ladder when the joint is in a planar state while achieving the motion of a CORE when in the deployed state. The second configuration constrains all degrees of freedom to create a static structure when the joint is in the planar state and allows for the motion of a CORE in the deployed state. Curved-folding origami techniques can be used with both configurations to control the cam radius and range of motion of the D-CORE. Physical models are demonstrated in Tyvek®, polycarbonate, polypropylene, and metallic glass. A deployable translating platform constructed of an inversion of the D-CORE is also shown.

Understanding Jacob's Ladder through The Tibetan Book of the Dead

Abstract: This article examines the correlations between the movie Jacob's Ladder and The Great Book of Natural Liberation through Understanding in the Between, or what is most often referred to as The Tibetan Book of the Dead. Directed by Adrian Lyne and starring Timothy Robbins, Jacob's Ladder confused audiences and critics alike upon its release in 1990. While it may be possible to interpret the movie from a biblical angle, given the title and names of some of the characters, we believe Jacob's Ladder is better understood using The Tibetan Book of the Dead as a guide. The film addresses death, coming to terms with its inevitability, and the need to see through the trappings of the ego, all of which serve as the basis behind the imagery and teachings of The Tibetan Book of the Dead.

Chemistry. Climbing Jacob's ladder.

Protein design enables the stabilization of a transient molecular state [Also see Report by Pearson et al. ]

A thorough understanding of the Diels–Alder reaction of 1,3‐butadiene and ethylene

The Diels–Alder (DA) reaction is one of the most important reactions in organic chemistry. The controversy surrounding this reaction as to whether it follows a concerted or stepwise mechanism has existed for a long time. The reaction of 1,3‐butadiene and ethylene is the paradigmatic example of the DA reaction. We have reinvestigated the mechanism of this reaction using density functional theory. The theoretical study considered all types of possible pathways for the reaction of 1,3‐butadiene and ethylene using six functionals at different rungs of Jacob's ladder. Therefore, a complete picture is given for a thorough understanding of the iconic DA reaction, and a new stationary point during the reaction processes has been reported for the first time. The calculated results indicated that three functionals, ωB97X‐D, M06‐2X, and B2‐PLYP, of the fourth and fifth rungs of Jacob's ladder performed well in the investigation of the mechanism of this reaction and that the reliable basis set should be larger than 6‐311+G(2d,p). The cis‐1,3‐butadiene more easily reacted with ethylene compared with 1,3‐butadiene in the trans conformation. The concerted mechanism was found to be energetically favorable, whose energy barrier is around 10 kcal/mol lower than that of the stepwise mechanism. Two investigated solvents, toluene and CH3CN, had little impact on this simple DA reaction. Copyright © 2014 John Wiley & Sons, Ltd.

A balanced procedure for the treatment of cluster–ligand interactions on gold phosphine systems in catalysis

Ligand-protected metal clusters are difficult to describe within density functional theory due to the need to treat the electronic structure of the cluster, possible charge transfer between the ligands and the cluster, and weak ligand-ligand interactions in a balanced manner. We demonstrate the use of an appropriate, stepwise benchmarking process that accounts for the nonadditivity of these different contributions to stability and catalytic activity. We consider both open- and closed-shell clusters, differently charged systems, and ligands of increasing complexity for gold phosphine systems. The use of a dispersion correction to density functional calculations was found to be crucial for both structure optimization and the calculation of binding energies. We find that PBE-D3 performs well with a variation in energetics of 0.7-10.9 kcal/mol, PBE0-D3 better with 0.0-3.3 kcal/mol, and B2PLYP-D3 the best with 0.2-2.4 kcal/mol, when compared to the best available benchmark [CCSD(T) or SCS-MP2]. Our systematic procedure clarifies that these functionals all give accurate results for certain cases, but for the total performance over a range of interactions, they perform in accordance with Jacob's ladder.

"Gulch," "Jacob’s Ladder," "Salt of the Earth," "Weathervane"

"Gulch," "Jacob’s Ladder," "Salt of the Earth," "Weathervane"