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.     

Study on the excitation mechanism 1. Non-Boltzmann–Saha distributions in the inductively coupled plasma

This work has further shown that the collisional–radiative multi-level model for the analyte atom and ion could be approximated by the step-wise series model. The non-Boltzmann and non-Saha factors of Ca for 48 levels corresponding to radiative decay, radiative recombination, Penning ionization and absorption processes, respectively, as well as to their mutual processes occurring at the axial channel of inductively coupled plasma and at an observation height of 15 mm above the load coil, were calculated. It was found that the high level relative to low level is over populated.     

Lattice cluster theory of associating polymers. II. Enthalpy and entropy of self-assembly and Flory-Huggins interaction parameter χ for solutions of telechelic molecules

The lattice cluster theory for solutions of telechelic polymer chains, developed in paper I, is applied to determine the enthalpy Δh(p) and entropy Δs(p) of self-assembly of linear telechelics and to evaluate the Flory-Huggins (FH) interaction parameter χ governing the phase behavior of these systems. Particular focus is placed on examining how these interaction variables depend on the composition of the solution, temperature, van der Waals and local "sticky" interaction energies, and the length of the individual telechelic chains. The FH interaction parameter χ is found to exhibit an entropy-enthalpy compensation effect between the "entropic" and "enthalpic" portions as either the composition or mass of the telechelic species is varied, providing unique theoretical insights into this commonly reported, yet, enigmatic phenomenon.     

Complexes of type C6H7(+)·L (L = N2 and CO2) studied by explicitly correlated coupled cluster theory

Complexes of the benzenium ion (C(6)H(7)(+)) with N(2) or CO(2) have been studied by explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x = a, b) level [T. B. Adler et al., J. Chem. Phys. 127, 221106 (2007)] and the double-hybrid density functional B2PLYP-D [T. Schwabe and S. Grimme, Phys. Chem. Chem. Phys. 9, 3397 (2007)]. Improved harmonic vibrational wavenumbers for C(6)H(7)(+) have been obtained by CCSD(T?)-F12a calculations with the VTZ-F12 basis set. Combining them with previous B2PLYP-D anharmonic contributions we arrive at anharmonic wavenumbers which are in excellent agreement with recent experimental data from p-H(2) matrix isolation IR spectroscopy [M. Bahou et al., J. Chem. Phys. 136, 154304 (2012)]. The energetically most favourable conformer of C(6)H(7)(+)·N(2) shows a π-bonded structure similar to C(6)H(7)(+)·Rg (Rg = Ne, Ar) [P. Botschwina and R. Oswald, J. Phys. Chem. A 115, 13664 (2011)] with D(e) ≈ 870 cm(-1). For C(6)H(7)(+)·CO(2), a slightly lower energy is calculated for a conformer with the CO(2) ligand lying in the ring-plane of the C(6)H(7)(+) moiety (D(e) ≈ 1508 cm(-1)). It may be discriminated from other conformers through a strong band predicted at 1218 cm(-1), red-shifted by 21 cm(-1) from the corresponding band of free C(6)H(7)(+).     

Metallorganische π-liganden: cluster als tripeldeckerkomplexe

Clusters (R′P)(RCCR)Fe₃(CO)₉ (1) have a pentagonal pyramidal cage structure with a planar C₂Fe₂P cycle acting as a organometallic 4π ligand towards a side-on η⁵-coordinated Fe(CO)₃ entity. Compounds of this type, which may be considered halfsandwich complexes, undergo transformation to clusters (R′P)(RCCR)Fe₄(CO)₁₁ (2) which correspond to triple-decker compounds with a planar central C₂Fe₂P 4π ligand. Compounds 2 can also be described as pentagonal bipyramidal clusters.Since compounds 1 are chemically related to a number of different cage molecules containing a C₂PFe₃ core and also to binuclear complexes with a C₂PFe₂ core, the triple-decker clusters 2 can also be prepared from these starting materials. Several examples of this type are given. The isoelectronic analogy between RP and S as cluster constituents is exemplified by the synthesis of a sulfur-containing analogue of 2 by similar procedures.     

“Short-bite” ligands in cluster synthesis

The short-bite ligands CH₂(PR ₂)₂ or CH(PR ₂)₃ (R = Me, Ph),RN(PX ₂)₂ (R=H, Me, Et;X = F, OR (R= Me, Et, i-Pr, Ph), Ph),RE(CH₂ ER₂)₂ (E = P, As;R = Me, Ph ), Ph₂ P(2-C₅H₄N) and related species are particularly versatile for the synthesis of di- and polynuclear complexes which frequently possess metal-metal bonds. In addition to homometallic products, these ligands often permit the directed synthesis of heterometallic complexes. Selected aspects of the chemistry of these complexes are also reviewed.     

Scanning vs. single spot laser ablation (λ=213 nm) inductively coupled plasma mass spectrometry

Sampling strategy is defined in this work as the interaction of a repetitively pulsed laser beam with a fixed position on a sample (single spot) or with a moving sample (scan). Analytical performance of these sampling strategies was compared by using 213 nm laser ablation ICP-MS. A geological rock (Tuff) was quantitatively analyzed based on NIST series 610-616 glass standard reference materials. Laser ablation data were compared to ICP-MS analysis of the dissolved samples. The scan strategy (50 μm/s) produced a flat, steady temporal ICP-MS response whereas the single spot strategy produced a signal that decayed with time (after 60 s). Single-spot sampling provided better accuracy and precision than the scan strategy when the first 15 s of the sampling time was eliminated from the data analysis. In addition, the single spot strategy showed less matrix dependence among the four NIST glasses.     

Determining the energy gap between the cis and trans isomers of HO3- using geometry optimization within the anti-Hermitian contracted Schrödinger and coupled cluster methods

The cis and trans isomers of the HO3- anion, which are important in proposed mechanisms for ozonization, are studied computationally. Relative energies, geometries, and normal-mode frequencies are calculated with anti-Hermitian contracted Schr?dinger equation (ACSE) and coupled cluster methods. Both the ACSE method and the coupled cluster method with single and double excitations (CCSD) are applied in a correlation-consistent polarized double-zeta basis set (cc-pVDZ). Using coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), we treat the problem with larger basis sets than those in previous work, including correlation-consistent polarized quadruple-zeta basis sets with (aug-cc-pVQZ) and without (cc-pVQZ) diffuse functions, which permit extrapolation of the cis and trans energies to the complete-basis-set limit. The cis isomer is found to be lower in energy than the trans isomer by -3.5 kcal/mol, which is 50% larger in magnitude than the best previous result of -2.2 kcal/mol. The bond lengths between the O2 and OH fragments of the cis- and trans-HO3 are calculated to be 1.713 and 1.857 A, respectively, where both bond lengths are significantly longer than the 1.464 A O-O bond in hydrogen peroxide. In this paper, we extend the ACSE method [Mazziotti, D. A. J. Chem. Phys. 2007, 126, 184101], which computes the two-electron reduced density matrix directly, to include geometry optimization by a Newton's method with numerical derivatives. Calculation of the cis- and trans-HO3- isomers by the ACSE yields energies, geometries, and frequencies that are closer to those from CCSD(T) than those from CCSD.     

Cr cluster deposition by plasma—gas-condensation method

Transmission electron microscopy observation was carried out for nanometric Cr clusters deposited on microgrids at room temperature using plasma–gas-condensation (PGC) method. In order to obtain optimum conditions for monodisperse cluster formation we have studied effects of an Ar gas pressure, an Ar gas flow rate, and a mixing rate of He gas with Ar gas on the size distribution of formed clusters. It has been found that monodisperse clusters with the size rage of 9–13 nm in diameter are producible at a low Ar gas pressure (≤1.3 Torr) and a low Ar gas flow rate (≤600 sccm). The mean cluster size decreases with decreasing Ar gas pressure, while it is not sensitive to the Ar gas flow rate. When He gas is mixed with Ar gas, the mean cluster size further decreases to 6 nm and the cluster beam intensity becomes stronger probably because He gas with the high thermal conductivity enhances supersaturation for cluster nucleation.     

Engineering therapeutic antibodies targeting G-protein–coupled receptors

G-protein–coupled receptors (GPCRs) are one of the most attractive therapeutic target classes because of their critical roles in intracellular signaling and their clinical relevance to a variety of diseases, including cancer, infection and inflammation. However, high conformational variability, the small exposed area of extracellular epitopes and difficulty in the preparation of GPCR antigens have delayed both the isolation of therapeutic anti-GPCR antibodies as well as studies on the structure, function and biochemical mechanisms of GPCRs. To overcome the challenges in generating highly specific anti-GPCR antibodies with enhanced efficacy and safety, various forms of antigens have been successfully designed and employed for screening with newly emerged systems based on laboratory animal immunization and high-throughput-directed evolution.     

Chemical bond between Cu(II) and Rn: ab initio study of CuRn n 2+ (n = 1–6) by coupled cluster method

Quantum chemical calculations of the structures, stabilities, and interactions of the title series at the CCSD(T) theoretical level are performed. The analysis of binding energies, average binding energies, and fragmentation energies indicate that the n = 2 system is more stable than its neighbors. Topological analysis of the natural bond orbital, electron density deformation, integrated charge transfer, bond critical point properties, reduced density gradient analysis are performed to explore the nature of the interaction. The results show that the present Rn–Cu²⁺ interactions fall into intermediate interaction type with a pronounced covalent character.     

SPC cluster modeling of metal oxides: ways of determining the values of point charges in the embedded cluster model

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How important are temperature effects for cluster polarizabilities?

State-of-the-art first-principle all-electron density functional theory calculations on small sodium clusters are performed to study the temperature dependency of their polarizabilities. For this purpose Born-Oppenheimer molecular dynamics simulations with more than 100,000 time steps (>200 ps) are recorded employing gradient corrected functionals in combination with a double-zeta valence polarization basis set. For each cluster 18 trajectories between 50 and 900 K are collected. The cluster polarizabilities are then calculated along these trajectories employing a triple-zeta valence polarization basis set augmented with field-induced polarization functions. The analysis of these calculations shows that the temperature dependency of the sodium cluster polarizabilities varies strongly with cluster size. For several clusters characteristic changes in the polarizability per atom as a function of temperature are observed. It is shown that the inclusion of finite temperature effects resolves the long-standing mismatch between calculated and measured sodium cluster polarizabilities.     

Chemistry of iridium carbonyl cluster complexes. Synthesis,characterization and solid state structure of the phosphido carbonyl cluster [Ir6(CO)12(μ-CO)2(μ-PPh2)−

The phosphido-bridged cluster [Ir₆(CO)₁₄ PPh2]^– has been obtained by reaction of [Ir₆(CO)₁₅]^2– with PHPh₂, in the presence of ferrocenium cation, followed by deprotonation. The anion was isolated as a salt of [N(PPh₃)₂]⁺ or K⁺ and its structure was determined by single crystal X-ray data analysis. The salt [N(PPh₃)₂][Ir₆(CO)₁₄PPh₂] crystallizes in the triclinic space group P witha = 11.835(1) Å,b = 15.007(1) Å,c = 18.766(2)_ Å; = 78.779(7)°, = 87.260(8)°, = 75.794(6)°,V = 3169.3(7) Å,Z = 2. The structure was solved by Direct Methods and Difference Fourier techniques and refined down toR andR _w values of 0.034 and 0.036, respectively, for 8003 observed reflections havingl > 3(I). The octahedral anion, of idealized C₂ symmetry, possesses two distance Ir-P = 2.284 Å, formally acting as a three electron donor. Average bond distances (Å) and angles (degrees) are: Ir-Ir = 2.776, Ir-C _t = 1.87, Ir-C _b = 2.05, C _t -O _t = 1.14, C _b -O_b= 1.17, Ir-P-Ir = 74.3°, Ir-C _t -O _t = 177°, Ir-C _b -O _b = 138°, Ir-C _b -Ir = 84° (t = terminal,b = bridging).