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1.
The theory of treating the configuration n0ln1lNn2l by means of nonorthogonal radial orbitals is described. The expressions for the matrix elements of the nonrelativistic Hamiltonian are deduced. A table that enables one to obtain these expressions in terms of radial integrals for l = 0 and 1 are given. Numerical calculations are performed for the configuration 1s22s22p3p using generalized hydrogen-like radial orbitals. The numerical values of the inter-term energy differences are given and discussed.  相似文献   

2.
Abstract

In solution, solute molecules B are coupled by attractive forces between them and all other molecules present; and these other molecules enhance the tension in the coupling force between solute molecules an amount πB, the osmotic pressure of the solution solute. Two equilibria determine the n o B moles of pure solute which dissolve in n 10 A moles of pure liquid solvent. If at T the solute is solid and in excess, then 1) the n B lsat moles of B in the nl A moles of A in a solution saturated with B are in thermodynamic equilibrium with the solid solute at the same T and p and 2) the n B lsat moles of B and nl A moles of A may also be in chemical equilibrium with the moles of new molecular or ionic species formed in the solution. Solute molecules dissolve until the chemical potential of the solution solute, pl B(T p, xB lsat), equals the chemical potential of pure solid solute at the same T and p, μ B so(T, p). When the solution is saturated with B and the mole fraction of B is xB lsat = n B lsat/σj n 1 j, then the vapor pressures of the solid solute at T and p, the solution solute at T and p, and the pure undercooled liquid solute at T and p-π B lsat are identical. If at T the n B lo moles of pure solute and the nl A moles of pure solvent are liquids, then if molecules of B are allowed to dissolve in A while molecules of A are dissolved in B, the resulting solutions may 1) contain only molecules of A and B or 2) contain A and B which also react to form other ionic and molecular species. The two solutions may be identical or they may differ. In all cases, however, the mole ratio of nl Bnl A in both solutions must be identical.  相似文献   

3.
For the 53 neutral atoms from He to Xe in their ground states, the average distances < u> n l , n l in position space and < v> n l , n l in momentum space between an electron in a subshell nl and another electron in a subshell n l are studied, where n and l are the principal and azimuthal quantum numbers of an atomic subshell, respectively. Analysis of 1700 subshell pairs shows that the electron-pair distances < u> n l , n l in position space have an empirical but very accurate linear correlation with a one-electron quantity U n l , n l L r +S r 2/(3L r ), where L r and S r are the larger and smaller of subshell radii < r> n l and < r> n l , respectively. The correlation coefficients are never smaller than 0.999 for the 66 different combinations of two subshells appearing in the 53 atoms. The same is also true in momentum space, and the electron-pair momentum distances < > n l , n l have an accurate linear correlation with a one-electron momentum quantity V n l , n l L p +S p 2/(3L p ), where L p and S p are the larger and smaller of average subshell momenta < p> n l and < p> n l , respectively. Trends in the proportionality constants between < u> n l , n l and U n l , n l and between < > n l , n l and V n l , n l are discussed based on a hydrogenic model for the subshell radial functions. Received: 8 April 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998  相似文献   

4.
 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A s n l λ, n l ′λ were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10−6 ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001  相似文献   

5.
The conformational characteristics of a comb‐like side‐chain liquid crystal polysiloxane (SCLCP), dissolved in deuterated chloroform, were evaluated by small‐angle neutron scattering (SANS) measurements over a wide q range. SANS studies were carried out on specimens with constant backbone length (DP = 198) and variable spacer length (n = 3, 5, and 11), and with constant spacer length (n = 5) and variable DP (45, 72, 127, and 198). The form factor P(q) at high q was analyzed using the wormlike chain model with finite cross‐sectional thickness (Rc) and taking into account the molecular weight polydispersity. The analysis generated values of persistence length in the range lp = 28–32 Å, considerably larger than that of the unsubstituted polysiloxane chain (lp = 5.8 Å), with contour lengths per monomer comparable to the fully‐extended polysiloxane backbone (lm = 2.9 Å). This indicates a relatively rigid SCLCP chain due to the influence of the densely attached mesogenic groups. The SCLCP with n = 11 is more flexible (lp = 28 Å) than those with n = 3 and n = 5 (lp = 32 Å). The cross‐sectional thickness increases with spacer length, Rcn0.21±0.02 (3 ≤ n ≤ 11), and the contour length per monomer decreases with increasing spacer length, lmn?0.35±0.01. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2412–2424, 2006  相似文献   

6.
An expression for the product of a single-cycle class [(1)N - P(p)]N and an arbitrary class [(1)l1(2)l …? (N)lN]N of the symmetric group has recently been conjectured. This expression involves a sum over a relatively small number of reduced class sums, depending on p indices. A further conjecture is formulated and demonstrated, according to which reduced class coefficients (RCCS ) involving cycles whose length is expressed by means of a single index can be related to corresponding coefficients in the product of [(1)N - P+1(p - 1)]N with an arbitrary class sum. Consequently, the problem of evaluating the general class sum product reduces to that of obtaining a relatively small set of fundamental RCCS containing no single-index cycles. The conjectures mentioned can be used to evaluate the product [(1)N - p(p)]N · [(1)N - q(q)]N in terms of fundamental RCCS that can all be obtained from the product [(r)]r · [(r)]r, where r = min(p, q). For the latter product, we use a result due to Boccara.  相似文献   

7.
Angular correlation coefficients τ nl,n^′ l^′ [p] between linear momenta of an electron in a subshell nl and another electron in a subshell nl′ are studied for the 102 neutral atoms He through Lr in their ground states, where n and l are the principal and azimuthal quantum numbers, respectively. We theoretically find that electron momenta are negatively correlated or uncorrelated; τ nl,n^′ l^′ [p] < 0 when |ll′|=1, while τ nl,n^′ l^′ [p]=0 when |ll′| ≠ 1. Numerical examinations of the atoms show that except for the He–B atoms, negative correlations are largest between 1s and 2p subshells, which have the most diffuse electron distributions in momentum space.  相似文献   

8.
Monodisperse micron-sized polystyrene particles crosslinked using urethane acrylate were produced by dispersion polymerization in ethanol solution and the effect of the crosslinked network structure on the polymerization procedure was studied. The influences of the concentrations of the initiator and urethane acrylate on the particle diameter (D n), the particle number density (N p), and the polymerization rate (R p) were found to obey the approximate relationships D n ∝ [initiator]0.43 [urethane acrylate]0.05, N p ∝ [initiator]−1.30 [urethane acrylate]0.19, and R p ∝ [initiator]0.24 ± 0.02. The power-law dependence of D n and N p on the initiator concentration showed a similar trend to that of linear polystyrene reported in the literature. Especially, it was found that urethane acrylate does not have a serious effect on D n and N p of the particles produced. The dependence of R p on the initiator concentration was observed to be higher than that of linear polystyrene, suggesting that there is still competition between heterogeneous polymerization and solution polymerization because of the crosslinked network structure of the primary particle. Received: 1 April 1999 Accepted in revised form: 29 June 1999  相似文献   

9.
Summary Experimental designs and non-linearly transformed factors (concentrations of analytes) have been applied in the Generalized Standard Addition Method (GSAM). The relationship betweenN measured analytical signals,R (1),...,R su(n), and concentrations of standard additions, c1,..., cn, ofn analytes has been approximated by the following polynomial models:The regression coefficientsB in models (1) are calculated from thesimple formulae1, 3, 4.Functionsf i (l) (e.g. linear, parabolic, exponential, hyperbolic or logarithmic) are selected on the basis of the experimentally determined relationshipsR (l) (l=1, ...,N) vs.c i (i=1, ...,n). An example concerns the flame emission photometric determination of Na and Ca. 22 factorial and uncomplete second-degree modelsR (l) have been applied expressed by linear and hyperbolic functionsf i (l). The results of determination of Na by GSAM reveal significant improvement of accuracy as compared with the conventional single-component standard addition method.
Nicht-lineare Transformation von Faktoren bei der verallgemeinerten Standardadditio nsmethode
Zusammenfassung Statistische Versuchsplanung und nicht-linear transformierte Faktoren (Konzentrationen der zu bestimmenden Substanzen) wurden für die verallgemeinerte Standardadditionsmethode eingesetzt. Die Bezeichnung zwischen N gemessenen analytischen Signalen,R (1),...,R (N) und den Konzentrationen der Standardadditionszugaben Ci,..., C N , vonn zu bestimmenden Substanzen wurde durch Polynome des folgenden Typs approximiert: (wobei ). Die Funktionenf i (l) (z. B. lineare, parabolische, exponentielle, hyperbolische oder logarithmische) werden auf Basis experimentell bestimmter Abhängigkeiten festgelegtR (l) (l=1,...,N) gegen C i (l=1,...,N). Als Beispiel wird die Flammenemissionsbestimmung von Na und Ca herangezogen. Dabei wurden ein 22 faktorieller Versuchsplan und ein unvollständiges Polynom der Ordnung 2R (l) mit linearen und hyperbolischen Funktionenf i (l) angesetzt. Die Resultate der Na-Be-stimmung zeigen durch die Verwendung der verallgemeinerten Standard-addition signifikante Verbesserungen der Resultate gegenüber der Einkomponenten-Standardaddition.


The author thanks Doc. dr. hab. A. Parczewski for his helpful discussion and editorial comments during the preparation of this paper.  相似文献   

10.
Expressions are derived for the n-dependent, hydrogen-like relativistic corrections to the magnetic dipole and electric quadrupole radial hyperfine integrals of an arbitrary atomic state. Good agreement has been obtained earlier between these corrections and the relativistic Hartree-Fock results for s1/2 states. The agreement remains good for the p1/2 states. For the p3/2 states in heavier atoms the hydrogenic corrections still reproduce the Hartree-Fock trend. For the higher l values the agreement is poor. Numerical tables are given for 1 ≤ Z ≤ 100 for the s1/2, p1/2, and p3/2 magnetic dipole cases and the p3/2 quadrupole case.  相似文献   

11.
The goals and limitations of some clustering methods are briefly reviewed. In order to avoid the usual methods which are very demanding on computer time and space, a new scheme is proposed for updating (generation) of, and retrieval from, large data bases organized as binary trees. The method is based on calculation of three distances at any given vertex l on the level n, A(l,n) instead of two. The respective distances d1(X,Al), d2(X,Ar), d3(AlAr) are calculated between the input vector X and the left and right descendant of the vertex A(l,n), Al and Ar, respectively. The advantage of the method compared to the standard clustering methods or formation of hierarchal trees is that the required memory or computational time is reduced from N2 to approximately N log N (N is the number of clustering objects).  相似文献   

12.
In the copolymerization of monomers M1 and M2 which form polymer radicals of chain length n of N1n with electron on a M1 type and N2n with one on a M2 type, it is assumed that the specific rates of termination between N1n and N1n and N1s, N1n and N2s, and N2n and N2s are kα(ns)?a, kβ(ns)?a, and kγ(ns)?a, respectively, where kα, kβ, and kγ are the rate constants of reaction between segment radicals in the respective termination, and a is constant. The relation between kinetic chain length n? and polymerization rate Rp is derived as: 1/n? = 1/n?0 + const. (Rp)A(a), where n?0 is the kinetic chain length of the polymer formed by transfer and A (a) is unity (predominance of transfer) and 1/(1–2a) (no transfer). In the copolymerization between methyl methacrylate (M1) and styrene (M2) at 60°C, when Rp → 0, kr12/k12 + kr21/k21 = 5.9× 10?5 is obtained, where kr12 and kr21 are the rate constants of transfer of N1 to M2 and N2 to M1, and k12 and k21 are the rate constants of propagation of N1 to M2 and N2 to M1. In the absence of transfer, the a value is found to be 0.065 ± 0.008, from the relation between n? and Rp, regardless of the monomer composition. Such a value is also estimated by setting b = 0.72 in a = 0.153 (2b–1), where b is the constant in the Mark-Houwink equation. Further, the value of kβ is found to be 1.18 × 109l./mole-sec, which is comparable with the diffusion-controlled rate of reaction between small molecules. The rate of reaction between segment radicals is fivefold larger than the polymer-polymer termination when transfer predominates.  相似文献   

13.
The dielectric spectra of polypropyleneglycols H-(C3H6O) N p -OH (PPGs), where N p = 1, 2, 3, 7, 12, 17, 20, 34, 69, were analyzed in terms of the Dissado Hill (DH) cluster model above the vitrification temperatures. In PPGs, the structural clusters are associates formed by intra- and intermolecular hydrogen bonds. The activation processes of cleavage and formation of intermolecular hydrogen bonds in clusters, when the total number of intermolecular hydrogen bonds changes, are characterized by the parameter n DH. The fluctuation processes of simultaneous exchange of molecules between adjacent clusters correspond to redistributions of intermolecular hydrogen bonds between clusters, when only the position but not the total number of intermolecular hydrogen bonds changes, and are characterized by the parameter m DH. The relaxation time τDH at 303 K and 423 K and the parameters n DH and m DH of the dielectric spectra were calculated. The activation energies of relaxation in the range 210–323 K were determined. The mean statistic squares of the dipole moments of clusters 〈μc2〉 and di-PG, PPG-425 (N p = 7), and PPG-2025 (N p = 34) molecules 〈μm2〉 at 303 K and 423 K were calculated. The number of the units of the oxypropylene chains involved in relaxation was determined. The dependence of the parameters of the DH model, relaxation energies, 〈μc2〉 and 〈μm2〉 on N p were studied.  相似文献   

14.
 The size-consistent self-consistent matrix dressing method has been applied on an open-shell single-configuration reference state. Once the reference state is converged, several low-lying roots can be obtained for the dressed configuration interaction (CI) matrices of appropriate symmetry. The CI matrices were built with a complete-active-space singles and doubles CI method in order to deal properly with multiconfiguration excited states. The vertical ionization and ionization–excitation transitions are obtained from the difference to the closed shell ground-state energy of the neutral molecule. The method has been applied to NH+ 3 and N+ 2 using atomic natural orbital basis sets and state-average adapted molecular orbitals. Two 2A1 states, very similar and showing great mixing of the (2a l −1) and (3a l −25a l 1) determinants, can be assigned to the broad asymmetric band at 27.6 ± 2 eV in the photoelectron spectrum of NH3. The possible contribution of a 2Π g (3σ g −2 g 1) state to the A shake-up peak of N2 at 24.6 eV is also discussed. Other states, doublets and quadruplets, are reported for both systems up to 30 eV for NH3 and 37 eV for N2. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000  相似文献   

15.
The atoms and ions in the electronic configurations 1s22s22pN (N = 2, 3, 4, 5, 6) are examined. N hydrogen-like radial orbitals for 2p electrons were used. The calculated energies of the 2p shell are compared with those of the ordinary method and with experimental results. The intermultiplet separation ratios are considered as well.  相似文献   

16.
4,4′‐(p‐Phenylene)bipyridazine, C14H10N4, (I), and the coordination compounds catena‐poly[[dibromidocopper(II)]‐μ‐4,4′‐(p‐phenylene)bipyridazine‐κ2N2:N2′], [CuBr2(C14H10N4)]n, (II), and catena‐poly[[[tetrakis(μ‐acetato‐κ2O:O′)dicopper(II)]‐μ‐4,4′‐(p‐phenylene)bipyridazine‐κ2N1:N1′] chloroform disolvate], {[Cu2(C2H3O2)4(C14H10N4)]·2CHCl3}n, (III), contain a new extended bitopic ligand. The combination of the p‐phenylene spacer and the electron‐deficient pyridazine rings precludes C—H...π interactions between the lengthy aromatic molecules, which could be suited for the synthesis of open‐framework coordination polymers. In (I), the molecules are situated across a center of inversion and display a set of very weak intermolecular C—H...N hydrogen bonds [3.399 (3) and 3.608 (2) Å]. In (II) and (III), the ligand molecules are situated across a center of inversion and act as N2,N2′‐bidentate [in (II)] and N1,N1′‐bidentate [in (III)] long‐distance bridges between the metal ions, leading to the formation of coordination chains [Cu—N = 2.005 (3) Å in (II) and 2.199 (2) Å in (III)]. In (II), the copper ion lies on a center of inversion and adopts CuN2Br4 (4+2)‐coordination involving two long axial Cu—Br bonds [3.2421 (4) Å]. In (III), the copper ion has a tetragonal pyramidal CuO4N environment. The uncoordinated pyridazine N atom and two acetate O atoms provide a multiple acceptor site for accommodation of a chloroform solvent molecule by trifurcated hydrogen bonding [C—H...O(N) = 3.298 (5)–3.541 (4) Å].  相似文献   

17.
《Analytical letters》2012,45(18):3417-3429
Abstract

A flow‐injection spectrophotometric procedure was developed for determining N‐acetylcysteine in pharmaceutical formulations. The sample was dissolved in deionized water and 400 µl of the solution was injected into a carrier stream of 1.0×10?2 mol l?1 sodium borate solution. The sample flowed through a column (70 mm length×2.0 mm i.d.) packed with Zn3(PO4)2 immobilized in a polymeric matrix of polyester resin and Zn(II) ions were released from the solid‐phase reactor because of the formation of the Zn(II) (N‐acetylcysteine)2 complex. The mixture merged with a stream of borate buffer solution (pH 9.0) containing 5.0×10?4 mol l?1 Alizarin red S and the Zn(II)Alizarin red complex formed was measured spectrophotometrically at 540 nm. The analytical curve was linear in the N‐acetylcysteine concentration range from 3.0×10?5 to 1.5×10?4 mol l?1 (4.9 to 24.5 µg ml?1) with a detections limit of 8.0×10?6 mol l?1 (1.3 µg ml?1). The relative standard deviations (RSDs) were smaller than 0.5% (n=10) for solutions containing 5.0×10?5 mol l?1 (8.0 µg ml?1) and 8.0×10?5 mol l?1 (13.0 µg ml?1) of N‐acetylcysteine, and the analytical frequency was 60 determinations per hour. A paired t‐test showed that all results obtained for N‐acetylcysteine in commercial formulations using the proposed flow‐injection procedure and a comparative procedure agreed at the 95% confidence level.  相似文献   

18.
Three novel vic-dioxime ligands containing the 1,8-diamino-3,6-dioxaoctane group, N,N′-(1,8-diamino-3,6-dioxaoctane)-p-tolylglyoxime (L1SL1H4), N,N′-(1,8-diamino-3,6-dioxaoctane)-phenylglyoxime (L2SL2H4), and N,N′-(1,8-diamino-3,6-dioxaoctane)-glyoxime (L3SL3H4) have been prepared from 1,8-diamino-3,6-dioxaoctane with anti-p-tolylchloroglyoxime, anti-phenylchloroglyoxime or anti-monochloroglyoxime. Polynuclear complexes [M(L x SL x )] n or [M(L x SL x )(H2O)] n (x = 1, 2 and 3), where M = CuII, CoII, and NiII, have been obtained with 1:1 metal/ligand ratio. The CuII and NiII poly-metal complexes of these ligands are proposed to be square planar, while also the prepared CoII complexes are proposed to be octahedral with two water molecules as axial ligands. The detection of H-bonding in the [Ni(L1SL1)] n , [Ni(L2SL2)] n and [M(L3SL3)(H2O)] n metal complexes by FT i.r. spectra revealed the square planar or octahedral [MN4·H2O)] n coordination of poly-nuclear metal complexes. [MN4] n coordination of the [Ni(L1SL1)] n and [Ni(L2SL2)] n complexes were also determined by 1H-n.m.r. spectroscopy. The ligands and poly-metal complexes were characterized by elemental analyses, FT-i.r., u.v.-vis., 1H and 13C-n.m.r. spectra, magnetic susceptibility measurements, molar conductivity, cyclic voltammetry, and differential pulse voltammetric (DPV) techniques.  相似文献   

19.
The photodissociation of gaseous molecular nitrogen has been investigated intensively, but the corresponding knowledge in a solid phase is lacking. Irradiation of pure solid nitrogen at 3 K with vacuum‐ultraviolet light from a synchrotron produced infrared absorption lines of product l‐N3 at 1657.8 and 1652.6 cm?1. The threshold wavelength to generate l‐N3 was determined to be (143.7±1.8) nm, corresponding to an energy of (8.63±0.11) eV. Quantum‐chemical calculations support the formation of l‐N3 from the reaction N2+N2, possibly through an activated complex l‐N4 upon photoexcitation with energy above 8.63 eV. The results provide a possible application to an understanding of the nitrogen cycle in astronomical environments.  相似文献   

20.
In the title cadmium(II) coordination polymer, poly[tri‐μ4‐adipato‐bis(2‐phenyl‐1H‐1,3,7,8‐tetraazacyclopenta[l]phenanthrene‐κ2N7,N8)tricadmium(II)], [Cd3(C6H8O4)3(C19H12N4)2]n, one of the Cd atoms is in a distorted pentagonal bipyramidal coordination environment, surrounded by five O atoms from three adipate (adip) ligands and two N atoms from one 2‐phenyl‐1H‐1,3,7,8‐tetraazacyclopenta[l]phenanthrene (L) ligand. A second Cd atom occupies an inversion center and is coordinated by six O atoms from six adip ligands in a distorted octahedral geometry. The carboxylate ends of the adip ligands link CdII atoms to form unique trinuclear CdII clusters, which are further bridged by the adip linkers to produce a two‐dimensional layer structure. Topologically, each trinuclear CdII cluster is connected to four others through six adip ligands, thus resulting in a unique two‐dimensional four‐connected framework of (4,4)‐topology. This work may help the development of the coordination chemistry of 1,10‐phenanthroline derivatives.  相似文献   

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