The density matrix in the two-particle function method

The first- and second-order density matrices D ^(N) and D for the function g⁽ⁿ⁾ = A_N[g(1, 2) …? g(N ? 1, N)] are expressed by the g function itself and its density matrix D . In a singlet state the generating functions for spatial parts of these matrices are simply connected with there solvent of the Fredholm equation in which the spatial part of D is a kernel. Some special cases of g(1, 2) are considered. It isestablished that the number of large eigenvalues of D does not exceed that of different eigenvalues of D . Thus the degeneracy in the spectrum of D causes the appearance of such large eigenvalues.     

New derivation of the Waller–Hartree–Fock spatial wave function

A new derivation is given for the Waller–Hartree–Fock double-determinantal spatial wave function. One starts from the single-determinant wave function in which a orbitals are doubly occupied, and decomposes it into a sum of products of spatial and spin functions. The spatial product of the first genealogical spin eigenfunction is a double-determinantal function. The derivation is based on the simple form of U_1?(P) when the representation matrix is obtained from the genealogical spin eigenfunction.     

X-ray spectroscopic study of the electronic structure of boron carbonitride films obtained by chemical vapor deposition on Co/Si and CoO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>/Si substrates

Boron carbonitride films are synthesized by chemical vapor deposition from a mixture of triethylamine borane and ammonia on a metallic or oxidized cobalt sublayer sprayed over Si(100) substrates. Scanning electron microscopy shows that the surface of a BC _x N _y /Co/Si sample has a homogeneous fine-grained structure; filamentous entities are found on the surface of the BC _x N _y /CoO _x /Si sample. The electronic structure of the films is investigated by X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure spectroscopy (NEXAFS). An analysis of the spectra shows that BC _x N _y films are composed of graphite and hexagonal boron nitride (h-BN) regions and complex BC _x N _y O _z components with B-C, N-C, B-O, N-O, and C-O bonds. The deposition of the BC _x N _y film on the oxidized Co sublayer results in an increase in the number of C-O, N-O, B-O, and C-N bonds and a decrease of the graphite and h-BN components and in the number of C-B bonds. The XPS data are used to estimate the surface elemental composition of the BC _x N _y /CoO _x /Si sample. It is found that the film consists of 66 at.% graphite component and 3 at.% h-BN; the proportion of complex C_0.46B_0.11N_0.05O_0.38 components is 31 at.%.     

Implementation of proficiency testing schemes for a limited number of participants

A metrological background for the selection and use of proficiency testing (PT) schemes for a limited number N of laboratories-participants (less than 20–30) is discussed. The following basic scenarios are taken into account: (1) adequate matrix certified reference materials (CRM) or in-house reference materials (IHRM) with traceable property values are available for PT use as test items; (2) no appropriate matrix CRM is available, but a CRM or IHRM with traceable property values can be applied as a spike or similar; (3) only an IHRM with limited traceability is available. The discussion also considers the effect of a limited population of PT participants N _p on statistical assessment of the PT results for a given sample of N responses from this population. When N _p is finite and the sample fraction N/N _p is not negligible, a correction to the statistical parameters may be necessary. Scores suitable for laboratory performance assessment in such PT schemes are compared. Presented at the 3rd International Conference on Metrology, November 2006, Tel Aviv, Israel.     

Approximate separation of the hyperradius in the many-particle Schrödinger equation

For large values of d = 3N, the radial distribution function of an N-particle system is sharply peaked near the hyperradius r_m = (d ? 2)/2k₀, where k₀≡(2/E/)^1/2. This fact allows an approximate separation of the hyperradius, leading to many-dimensional hydrogenlike radial solutions. Kindred applications to dimensional scaling are also discussed, where d = DN, with D the spatial dimension. For the large D regime, illustrative analytic formulas are obtained giving the energy and effective nuclear charge for the lowest few S states of the helium atom.     

Hydrogen‐bonding network of N,N′‐bis[2‐(tert‐butyldimethylsiloxy)ethyl]ethylenediammonium dichloride

The title salt, C₁₈H₄₆N₂O₂Si₂²⁺·2Cl⁻, has been synthesized by reaction of N,N′‐bis(2‐hydroxyethyl)ethylenediamine with tert‐butyldimethylsilyl chloride. The zigzag backbone dication is located across an inversion centre and the two chloride anions are related by inversion symmetry. The ionic components form a supramolecular two‐dimensional network via N—H...Cl hydrogen bonding, which is responsible for the high melting point compared with the oily compound N,N′‐bis[2‐(tert‐butyldimethylsiloxy)ethyl]ethylenediamine.     

Toward a quantitative theory of the rheology of concentrated solutions of stiff polymers

Predictions of the rheological properties of concentrated isotropic solutions of stiff polymers are made that improve on those obtained with the approximate Doi theory. Predictions of the shear-rate and concentration dependence of the viscosity η and the first and second normal stress differences N₁ and N₂ that avoid the closure approximations of Doi are obtained by using a Galerkin numerical solution for the orientation distribution function. The predictions for η and N₁, though they neglect the effects of polydispersity in molecular weight, are shown to be in quantative agreement with recent measurements on solutions of poly-γ-benzyl-L -glutamate (PBLG). The polydispersities of a series of commercial PBLG and PBDG samples are measured by gel permeation chromatography, and found to be broad. An attempt is made to account for the effects of polydispersity on the linear viscoelastic storage and loss moduli for PBLG solutions by using the Marrucci–Grizzuti extension of the Doi theory. The attempt fails. The most probable explanation for the failure is that the rotary diffusive motions of the shorter molecules in the mixture are drastically slowed by the matrix of surrounding longer molecules.     

The spin-orbit interaction in the configuration nlN n'l using nonorthogonal radial orbitals

Formulas for the calculation of matrix elements of the simplified operator of the spin-orbit interaction for the configuration n₁l^Nn₂l are deduced for the case when radial orbitals are nonorthogonal. The coefficients of the radial integrals are tabulated for the configuration p^Np. The fine structure of the excited configuration of the carbon atom is calculated.     

Structure and spin-purity conditions for reduced density matrices of arbitrary order

For arbitrary k, the separation of spin variables is performed in the reduced density matrix of the kth order (RDM -k) on the basis of the Fock coordinate function method. The independent spatial components of RDM -k are analyzed. For RDM -k of the total spin eigenstate, their number is proved never to exceed its spin multiplicity 2s + 1. Integral and other nontrivial interrelations between spatial components are established which turn out to be the necessary and sufficient conditions of spin purity of a wavefunction corresponding to a given RDM -k. It is shown that the r-rank k-particle spin distribution matrix F, defined as a spatial coefficient at the spin-tensorial operator of rank r in the RDM -k expansion, can be obtained by reduction of the (k + r)-particle charge density matrix F. In particular, all spatial components of RDM -2 are explicitly expressed in terms of the four-electron charge density matrix only. This allows us to purpose some approximative formulas for the McWeeny-Mizuno spin–orbit and spin–spin coupling functions in the case of the weak spin contamination.     

Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene π-electron models

Methods accounting for correlation effects in quasi-one-dimensional π-electron systems and based on the restricted Hartree–Fock (RHF ) single determinantal reference state are briefly reviewed as well as their role in the bond length alternation (or dimerization) problem in polyactylene-like systems, as described by the semiempirical Hamiltonians of the Pariser–Parr–Pople (PPP ) type. Particular attention is given to the π-electron model of cyclic polyene homologous series C_NH_N, N = 2n = 4v + 2, v = 1,2,…, which can be regarded as an idealized model of one-dimensional metallic-like systems with imposed Born–von Kármán boundary conditions when N ∞. These models provide a useful bridge between the typical aromatic systems, represented by benzene (N = 6) π-electron model, and long linear polyenic chains, since the properties of these systems hardly change once a sufficiently large N (?26 or 30) is reached. It is shown that due to the quasidegenerate character of the RHF reference employed, and the related prominence of connected quadruply excited cluster components in the exact wave function, most of the standard technieques suffer a singular behavior break down entirely for large enough systems, particularly in the strongly correlated regime. The approximate coupled pair theory that accounts for quadruply excited clusters (ACPQ method) is shown to be free of these shortcomings and is extended to include also approximately the effects of connected triexcited cluster components. These results are compared with other recently examined approximate methods accounting for the tri- and quadruply excited clusters and the proposed ACPQ +T (ACPQ ) procedure is shown to provide the best results in the whole range of the coupling constant.     

[2,6‐Bis(1H‐benzimidazol‐2‐yl‐κN3)­pyridine‐κN](di­methyl­form­amide‐κO)­(thio­sulfato‐κ2O,S)­nickel(II) mono­hydrate

The structure of the title compound, [Ni(ths)(bbip)(dmf)]·­H₂O [ths is thio­sulfate, S₂O₃; bbip is 2,6‐bis(1H‐benz­imidazol‐2‐yl)­pyridine, C₂₁H₁₃N₅; and dmf is di­methyl­form­amide, C₃H₇NO], is monomeric, with the nickel ion octahe­drally surrounded by an N,N′,N′′‐tridentate bbip mol­ecule, an S,O‐bidentate ths mol­ecule and an O‐monodentate dmf mol­ecule. The H atoms of the hydration water mol­ecule and the amino groups of bbip are involved in hydrogen bonding and determine a spatial organization of broad layers parallel to (001), which are connected by weak interactions.     

Integral–geometrical consideration of density matrices

The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM ) as well as the problem of reconstruction of the N-particle system density matrices (N-DM ) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators Θ are represented using particular values (at specially chosen ) of the Radon transform of the N-DM spatial parts (or their sums) ??_Nλ(x′ | x″) (here, is a d-plane in the n-space ?ⁿ of x = (x′, x″)), with n = 6N, d = 3 (N ? k), x′ ≡ (r′₁, ?, r′_N), x′ ≡ (r₁″, ?, r″_N ()). In this way, the problem is reduced to investigation of the properties of the functions . For a normalizable N – DM , it is proved that are bounded functions. The properties of implied by the N-DM permutational symmetry, Hermiticity, and positive definiteness are found. A formal procedure of reconstruction of all N-DM corresponding to a given k-RDM is proposed. © 1995 John Wiley & Sons, Inc.     

碳纳米管/聚氨酯杂化膜的原位聚合构建及气体渗透性能

采用H2SO4/HNO3混酸处理得到不同氧化程度的多壁碳纳米管(MWCNT-COOH),再通过与4,4′-二苯基甲烷二异氰酸酯(MDI)、1,4-丁二醇(BDO)的预聚和扩链反应构建碳纳米管/聚氨酯(MWCNT-COOH/PU)杂化膜。利用傅里叶红外光谱(FTIR)、拉曼光谱(Raman)和透射电子显微镜(TEM)等分析表征多壁碳纳米管结构;探讨了多壁碳纳米管氧化程度和填充量对MWCNTCOOH/PU杂化膜的形貌和CO2、N2渗透性能的影响。结果表明,混酸处理后的多壁碳纳米管带有一定的含氧基团,并随氧化程度的提高,多壁碳纳米管的拉曼光谱G峰和D峰的强度之比(ID/IG)有所增大;氧化程度对多壁碳纳米管在溶剂和杂化膜中的分散性有较大影响,氧化程度越高,分散性越好;杂化膜的CO2、N2渗透性及CO2/N2渗透选择性随多壁碳纳米管氧化程度的增加有所增大,而随多壁碳纳米管填充量的增加表现出先增大后减小的趋势,当氧化程度较高的多壁碳纳米管(H-MWCNT-COOH)填充量为1.0wt%时,H-MWCNT-COOH/PU杂化膜的CO2渗透系数为67.8 Barrer,CO2/N2渗透选择性可达45,表明适量填充MWCNT-COOH能显著提高MWCNT/PU杂化膜的CO2渗透性及CO2/N2的渗透选择性。     

Photoelectron spectra andab initio calculations of the electronic structure of amino-n-sulfenyl chlorides

The electronic structure of some amino-N-sulfenyl chlorides and related compounds is studied by photoelectron spectroscopy and ab initio calculations. Similar values of IP(n _S ) and IP(n _N ) and the total energy minimum indicate that in stable conformations the n _S and n _N orbitals are orthogonal. These conformers are characterized by an effective n_N-σ _S-Cl ^* interaction. The relationship between the intramolecular shift of charge and ionization potential values and the spatial structure of amino-N-sulfenyl chlorides is analyzed. A. E. Arbuzov Institute of Organic and Physical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 2, pp. 69–73, March–April, 1994. Translated by L. Smolina     

Graphical representation of the state of orientation of polymer systems

The orientation distribution function for noncrystalline structural units in polymer systems cannot be determined completely from any experimental source; only the second and/or fourth moments of the distribution function, i.e., the second and/or fourth orders of the generalized orientation factors F_lm^j, can be evaluated. It is there-fore necessary to estimate the distribution function from F_2m^j and F_4m^j. In this paper, a graphical representation of the state of orientation is first discussed in terms of plots of F₄₀^j against F₂₀^j for several types of distribution functions for uniaxial orientation. These are three types of extreme concentration of the distribution at particular polar angles θ₀ given by θ₀ = 0, 0<θ₀<π/2, and θ₀ = π/2; five types of rather realistic distributions having single maxima at θ_j = 0, θ₀, π/2 and double maxima at θ_j = 0, π/2, and a single minimum at θ_j = θ₀; and four types of more realistic distributions including Kratky's floating rod model in an affine matrix. Second, estimation of the distribution function for uniaxial orientation from F₄₀^j and F₂₀^j is discussed quantitatively in terms of the mean-square error by three approximation methods: (a) expansion of the distribution function in finite series of spherical harmonics through the fourth order, (b) approximation of the distribution function as a composite of two components, random orientation and a particular orientation distribution given by N_a (cos²θ_j)^a, N_a being a constant, and (c) approximation of the distribution function by N_a (cos²θ_j)^a alone. It is concluded that when the orientation distribution is sharp, estimation by the second method of approximation gives a smaller error than the first.     

Ab initio calculations on NO2 and NO 2 − : Optimization of diffuse Gaussian exponents

Ab initio calculations of NO₂ and NO ₂ ⁻ , using a Dunning [4s3p] basis augmented by 1 component diffuses andp functions were carried out. The SCF energies of NO₂ and NO_2/− (ground states) as a function of O _s , O _p , N _s , and N _p diffuse function exponents are given and discussed. The curves show some unexpected features which make the optimization of the diffuse function exponents problematic. The SCF vertical electron detachment energy for NO ₂ ⁻ as a function of the diffuse O _s , O _p , N _s , and N _p exponents is then discussed. Except for the case of O _p , the detachment energy is essentially independent of the O _s , N _s , and N _p exponents. Finally, results of SCF and MCSCF/CI calculations of the electron affinity of NO₂ are given and compared with experiment. Work performed under the auspices of the Division of Basic Energy Sciences of the U.S. Department of Energy. By acceptance of this article, the publisher and/or recipient acknowledges the U.S. Government's right to retain a nonexclusive, royalty-free license in and to any copyright covering this paper.     

Coordination polymer chains built from CuII and adipate ions linked by hydrogen bonds to form a three‐dimensional framework structure

In the title compound, catena‐poly[bis[(2,2′‐bipyridine‐κ²N,N′)(1,1,3,3‐tetracyano‐2‐ethoxypropenido‐κN)copper(II)]‐μ₄‐hexanedioato‐κ⁶O¹,O^1′:O¹:O⁶,O^6′:O⁶], [Cu₂(C₉H₅N₄O)₂(C₆H₈O₄)(C₁₀H₈N₂)₂]_n, the adipate (hexanedioate) dianion lies across a centre of inversion in the space group P. The Cu^II centre adopts a distorted form of axially elongated (4+2) coordination, and the Cu^II and adipate components form a one‐dimensional coordination polymer from which the 2,2′‐bipyridine and 1,1,3,3‐tetracyano‐2‐ethoxypropenide components are pendent, and where each adipate dianion is bonded to four different Cu^II centres. The coordination polymer chains are linked into a three‐dimensional framework structure by a combination of C—H...N and C—H...O hydrogen bonds, augmented by a π–π stacking interaction.     

The Radical Cation of Azatriquinane: An ESR Study

Azatriquinane (=10-azatricyclo[5.2.1.0^1,10]decane; 1 ) was oxidized to its radical cation 1 ^.+ by γ- irradiation in a CF₂ClCFCl₂ matrix at 77 K. A prominent feature of the ESR spectrum of 1 ^.+ is the ¹⁴N-hyperfine anisotropy which broadens the components with M_I(¹⁴N)=±1. The observed coupling constants are a_N=+ 2.5 and a_H=+ 4.0 mT for the ¹⁴N nucleus and the three methine β-protons, respectively. While the a_N value points to pyramidalization at the N-atom comparable to that in the radical cation of quinuclidine (=1-azabicyclo[2.2.2]octane; 4 ), an eclipsing of the singly occupied orbital at this atom by the three C−H_β bonds is indicated in view of the large a_H value. Theoretical calculations on the geometry of 1 ^.+ are in accord with the conclusions drawn from the experimental findings.     

Some developments in the spin-extended Hartree-Fock method

All the second-order density matrix spin components for the spin-extended Hartree-Fock method are obtained. The coefficients in the final formulae are only ω_sM, ω_sM±1, ω_sM±2, where ω_sM are the weights of pure states of spin s in the initial unprojected determinant with spin projection M. The eigenvalue problem for the best electron density natural orbitals in the spin-extended method is formulated. All the second-order transition density matrix spin components between pure spin basis functions built of orthogonal orbitals and distinguished by different core choice are also found. This basis may be used on CI calculations.