Behind the success of modified coupled-cluster methods: addition by subtraction

ABSTRACT

Modified coupled-cluster (CC) methods such as linearized coupled-cluster doubles (LinCCD), approximate coupled pair (ACP D14), 2CC (from nCC family), parameterized CCSD (pCCSD) and distinguishable cluster (DCSD) can have their advantages over general CC methods. Though these methods include connected clusters of single and double excitations at most, distinguishable cluster, parameterized CC and approximate coupled pair methods, in particular, have been shown to produce quantitatively correct results in benchmark studies. To put these methods on a stronger foothold, it is essential to understand the rationale for their success: mimicking the effect of connected triple excitations. We exploit the relation between CC and many body perturbation theory (MBPT) in general, and between CCSD and MBPT(4)/MP4 in particular, to take a step towards bringing clarity to this persisting conundrum. Our aim here is to look for numerical signs of ‘addition by subtraction’ or ‘inclusion by deletion’ effect that is likely behind the success of these modified CCD or CCSD methods. We achieve this by revisiting well-studied examples of single and multiple bond dissociation and comparing the performance of these modified CCSD methods with higher-level CC methods. Though our results are qualitative in nature, we hope this would lead to more rigorous analysis in future studies.     

Three bis‐ortho‐diynyl­arenes (BODA)

The molecule of 3,3′,4,4′‐tetrakis­(phenyl­ethynyl)­bi­phenyl, C₄₄H₂₆, is approximately planar and is located on a crystallographic inversion center. Bis­[3,4‐bis­(phenyl­ethynyl)­phenyl] ether, C₄₄H₂₆O, has mol­ecules located on twofold symmetry axes, whereas the molecule of 2,2‐bis­[3,4‐bis­(phenyl­ethynyl)­phenyl]­propane, C₄₇H₃₂, does not exhibit any molecular symmetry.     

Solid state studies of drugs and chemicals by dielectric and calorimetric analysis

Novel dielectric behavior of a linear increase in ionic conductivity prior to melt temperature was observed for active pharmaceutical ingredients (APIs), organic chemicals, amino acids, and carbohydrates. Though, there are solids like polyolefins and long chain organic compounds (tetracosane, pentacosane) which do not exhibit this premelt behavior (i.e., the temperature where the onset of increase in ionic conductivity to melt temperature). We have discovered novel electrical conductivity properties and other physical analytical variations which can lead to unique synthetic routes of certain chemical entities. The above-mentioned unique variations are not related to solid–solid transitions which are quite often observed in pharmaceutical crystalline solids. These new properties are related to amorphous crystalline behavior of a solid. We have also studied the effect of various experimental variables: such as amount of mass tested, applied frequency at a given electric field and heating rate, which results in varying the onset temperature of the increase in ionic conductivity. Melting of the solids was correlated using differential scanning calorimetry (DSC). Activation energies for all the solids were measured in the premelt region using an Arrhenius plot at a specific frequency since we observed changes in the conductivity with frequency. This study focused on frequencies 0.1 to 10 Hz, since the conductivity at these frequencies related to surface analysis. This new physical properties are leading to new electro synthetic procedures to modify or prepare chemicals.     

Thermally-induced dielectric relaxation spectra in three aldohexose monosaccharides

Three aldohexose monosaccharides, d-glucose, d-mannose, and d-galactose, were examined by scanning temperature dielectric analysis (DEA) from ambient temperatures through their melts. Phase transitions, including glass transition (T _g) and melting temperature (T _m), were evaluated by differential scanning calorimetry (DSC). The monosaccharides were found to exhibit thermally-induced dielectric loss spectra in their amorphous-solid phase before melting. Activation energies for electrical charging of each of the monosaccharides were calculated from an Arrhenius plot of the tan delta (e″/e′, dielectric loss factor/relative permittivity) peak frequency versus reciprocal temperature in Kelvin. The DEA profiles were also correlated with the DSC phase diagrams, showing the changes in electrical behavior associated with solid–solid and solid–liquid transitions.     

An experimental and theoretical study of competitive adsorption at the n-heptane/water interface

A model to calculate the interfacial concentration of competing surface active species in a two-phase oil/water system was developed. To enable the calculation of the surface excess of 2-hydroxy-5-nonylacetophenone oxime (HNAPO, active ingredient of LIX 84) in the presence of surfactants competing for interfacial area, an interfacial adsorption competition model was derived for noninteracting surface active species in a n-heptane/aqueous system, assuming ideal enthalpy and entropy of mixing. The model was found to be valid for HNAPO in the presence of sodium dodecyl sulfate (SDS) or dodecyldimethyl(3-sulfopropyl)ammonium (DDSA). In the case of dodecyltrimethylammonium chloride (DTAC) or octa(ethylene glycol) mono-n-dodecyl ether (C12E8) as the competing surfactants with HNAPO, the predicted surface excess values from the model fit less favorably. The difference was shown to not be due to nonideal entropy of mixing.     

Structure and dynamics of MG rubber studied by dynamic mechanical analysis and solid‐state NMR

Methyl‐methacrylate‐grafted natural rubber was prepared by free radical polymerization of methyl methacrylate in natural rubber latex, and their structure and dynamics were investigated by dynamic mechanical analysis and solid‐state nuclear magnetic resonance (NMR). Samples were prepared by chemical initiation and high‐energy radiation. The changes of glass transition temperature and tan δ max with different total poly(methyl methacrylate (PMMA) content are reported. The effect of the change in composition in copolymers on tan δ peak width, tan δ max, and area under the tan δ curve are used to understand the miscibility and damping properties. Solid‐state ¹³C‐NMR measurements were carried out to determine several relaxation time parameters, such as rotating frame and laboratory frame proton and carbon relaxation times. Cross polarization times and carbon relaxation times were interpreted based on the changes in the molecular motion. Proton relaxation times were interpreted based on the heterogeneity of the matrix. Results confirmed phase separation and a presence of an interfacial region. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1141–1153, 1999     

Purely infinite corona algebras of simple C*-algebras

In this paper, we study the problem of when the corona algebra of a non-unital C*-algebra is purely infinite. A complete answer is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the algebra, and to the behaviour of corona projections, despite the fact that there is no real rank zero condition.     

Exclusion limits on the WIMP-nucleon cross section from the cryogenic dark matter search

The Cryogenic Dark Matter Search (CDMS) employs Ge and Si detectors to search for weakly interacting massive particles (WIMPs) via their elastic-scattering interactions with nuclei while discriminating against interactions of background particles. CDMS data, accounting for the neutron background, give limits on the spin-independent WIMP-nucleon elastic-scattering cross section that exclude unexplored parameter space above 10 GeV/c2 WIMP mass and, at >75% C.L., the entire 3sigma allowed region for the WIMP signal reported by the DAMA experiment.     

Flow of an Oldroyd-fluid in a contracting channel with a moving boundary

The industrial process of coating flat surfaces with polymeric substances is numerically simulated by solving the full equations of motion for a flow through a contraction with a moving boundary. The four-constant Oldroyd constitutive equation is used to represent the viscoelastic fluid. Some adjustments to existing finite-difference methods are made in such a way as to avoid singular iterative matrices during the solution process. Results are presented for flow situations with Weissenberg numbers up to about three times larger than any previously published results for this problem.