The divide-expand-consolidate family of coupled cluster methods: numerical illustrations using second order Møller-Plesset perturbation theory

Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are term-wise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals. Evaluating the atomic site and pair interaction energies using local orbitals leads to a linear scaling algorithm and a distinction between Coulomb hole and dispersion energy contributions to the correlation energy. Further, a detailed error analysis is performed illustrating the error control imposed on all components of the energy by the chosen energy threshold. This error control is ultimately used to show how to reduce the computational cost for evaluating dispersion energy contributions in DEC.     

Auditory brainstem responses to chirps delivered by different insert earphones

The frequency response and sensitivity of the ER-3A and ER-2 insert earphones are measured in the occluded-ear simulator using three ear canal extensions. Compared to the other two extensions, the DB 0370 (Bru?el & Kj?r), which is recommended by the international standards, introduces a significant resonance peak around 4500 Hz. The ER-3A has an amplitude response like a band-pass filter (1400 Hz, 6 dB/octave -4000 Hz, -36 dB/octave), and a group delay with "ripples" of up to ±0.5 ms, while the ER-2 has an amplitude response, and a group delay which are flat and smooth up to above 10000 Hz. Both earphones are used to record auditory brainstem responses, ABRs, from 22 normal-hearing ears in response to two chirps and a click at levels from 20 to 80 dB nHL. While the click-ABRs are slightly larger for ER-2 than for ER-3A, the chirp-ABRs are much larger for ER-2 than for ER-3A at levels below 60 dB nHL. With a simulated amplitude response of the ER-3A and the smooth group delay of the ER-2 it is shown that the increased chirp-ABR amplitude with the ER-2 is caused by its broader amplitude response and not by its smoother group delay.     

Determining Yields in High Solids Enzymatic Hydrolysis of Biomass

As technologies for utilizing biomass for fuel and chemical production continue to improve, enzymatic hydrolysis can be run at still higher solids concentrations. For hydrolyses that initially contain little or no free water (10-40% total solids, w/w), the saccharification of insoluble polymers into soluble sugars involves changes of volume, density, and proportion of insoluble solids. This poses a new challenge when determining the degree of hydrolysis (conversion yield). Experiments have shown that calculating the yield from the resulting sugar concentration in the supernatant of the slurry and using the assumed initial volume leads to significant overestimations of the yield. By measuring the proportion of insoluble solids in the slurry as well as the sugar concentration and specific gravity of the aqueous phase, it is possible to precisely calculate the degree of conversion. The discrepancies between the different ways of calculating yields are demonstrated along with a nonlaborious method for approximating yields in high solids hydrolysis.     

Photoreactivity of biologically active compounds. XIX: Excited states and free radicals from the antimalarial drug primaquine

The formation and reactivity of excited states and free radicals from primaquine, a drug used in the treatment of malaria, was studied in order to evaluate the primary photochemical reaction mechanisms. The excited primaquine triplet was not detected, but is likely to be formed with a short lifetime (<50 ns) and with a triplet energy <250 kJ/mol as the drug is an efficient quencher of the fenbufen triplet and the biphenyl triplet, and forms ${}^1{\text{O}}_2$ by laser flash photolysis $({}^{\text{PQ}}{\Phi }_{\mathrm{\Delta }}=0.025)$. Primaquine (PQ) exists as the monocation $({\text{PQH}}^{+})$ in aqueous solution at physiological pH. ${\text{PQH}}^{+}$ photoionises by a biphotonic process and also forms the monoprotonated cation radical $({\text{PQH}}^{2+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}})$ by one electron oxidation by ${\text{HO}}^{\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}$ (k_q = 6.6 × 10⁹ M^?1 s^?1) and ${\text{Br}}_2^{\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}-}$ (k_q = 4.7 × 10⁹ M^?1 s^?1) at physiological pH, detected as a long-lived transient decaying essentially by a second order process (k₂ = 7.4 × 10⁸ M^?1 s^?1). ${\text{PQH}}^{2+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}$ is scavenged by O₂, although at a limited rate (k_q = 1.0 × 10⁶ M^?1 s^?1). The reduction potential (E°) of ${\text{PQH}}^{2+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}/{\text{PQH}}^{+}$ is < +1015 mV, as measured versus tryptophan (${\text{TRP}}^{\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}/\text{TRPH}$). Primaquine also forms ${\text{PQH}}^{2+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}$ at pH 2.4, by one electron oxidation by ${\text{Br}}_2^{\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}-}$ and proton loss (k_q = 2.7 × 10⁹ M^?1 s^?1). The non-protonated cation radical (${\text{PQ}}^{+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}$) is formed during one electron oxidation with ${\text{Br}}_2^{\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}-}$ at alkaline conditions (k_q = 4.2 × 10⁹ M^?1 s^?1 at pH 10.8). The estimated pK_a-value of ${\text{PQH}}^{2+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}/{\text{PQ}}^{+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}$ is pK_a ～ 7–8. Primaquine is not a scavenger of ${\text{O}}_2^{\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}-}$ at physiological pH. Thus self-sensitization by ${\text{O}}_2^{\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}-}$ is eliminated as a degradation pathway in the photochemical reactions. Impurities in the raw material and photochemical degradation products initiate photosensitized degradation of primaquine in deuterium oxide, prevented by addition of the ${}^1{\text{O}}_2$ quencher sodium azide. Photosensitized degradation by formation of ${}^1{\text{O}}_2$ is thus important for the initial photochemical decomposition of primaquine, which also proceeds by free radical reactions. Formation of ${\text{PQH}}^{2+\text{<mglyph src="https://sdfestaticassets-us-east-1.sciencedirectassets.com/shared-assets/16/entities/rad"></mglyph>}}$ is expected to play an essential part in the photochemical degradation process in a neutral, aqueous medium.     

Computer-simulated amorphous structures (I). Quenching of a Lennard-Jones model system

The molecular dynamics technique was used to study the thermodynamic and structural properties of non-crystalline solid structures. The structures were obtained by quenching a model liquid consisting of 336 atoms arranged in a computational cell with periodic boundaries and with the atomic intereaction represented by the Lennard-Jones pair potential. The characteristics of the resulting non-crystalline atomic configurations were found to depend weakly on the applied quenching rate.     

Measurement of antiproton lifetime using the ice storage ring

Antiprotons have been stored in the ICE Storage Ring and held for 85h with the help of stochastic cooling. We set a limit of at least 32 h for the antiproton lifetime (in its rest frame).     

Anisotropic relaxation and motion of half-integer quadrupole nuclei studied by central transition nuclear magnetic resonance spectroscopy

An efficient theoretical formalism and advanced experimental methods are presented for studying the effects of anisotropic molecular motion and relaxation on solid-state central transition NMR spectra of half-integer quadrupole nuclei. The theoretical formalism is based on density operator algebra and involves the stochastic Liouville–von Neumann equation. In this approach the nuclear spin interactions are represented by the Hamiltonian while the motion is described by a discrete stochastic operator. The nuclear spin interactions fluctuate randomly in the presence of molecular motion. These fluctuations may stimulate the relaxation of the system and are represented by a discrete relaxation operator. This is derived from second-order perturbation theory and involves the spectral densities of the system. Although the relaxation operator is valid only for small time intervals it may be used recursively to obtain the density operator at any time. The spectral densities are allowed to be explicitly time dependent making the approach valid for all motional regimes. The formalism has been applied to simulate partially relaxed central transition ¹⁷O NMR spectra of representative model systems. The results have revealed that partially relaxed central transition lineshapes are defined not only by the nuclear spin interactions but also by anisotropic motion and relaxation. This has formed the basis for the development of central transition spin-echo and inversion-recovery NMR experiments for investigating molecular motion in solids. As an example we have acquired central transition spin-echo and inversion-recovery ¹⁷O NMR spectra of polycrystalline cristobalite (SiO₂) at temperatures both below and above the α–β phase transition. It is found that the oxygen atoms exhibit slow motion in α-cristobalite. This motion has no significant effects on the fully relaxed lineshapes but may be monitored by studying the partially relaxed spectra. The α–β phase transition is characterized by structural and motional changes involving a slight increase in the Si–O–Si bond angle and a substantial increase in the mobility of the oxygen atoms. The increase in the Si–O–Si angle is supported by the results of ¹⁷O and ²⁹Si NMR spectroscopy. The oxygen motion is shown to be orders of magnitude faster in β-cristobalite resulting in much faster relaxation and characteristic lineshapes. The measured oscillation frequencies are consistent with the rigid unit mode model. This shows that solid-state NMR and lattice dynamics simulations agree and may be used in combination to provide more detailed models of solid materials.