Electron correlation effects in the 4f14 shell

This paper serves a twofold purpose. First, Löwdin's inner projection in both nonperturbative and perturbative forms is applied to the quartic anharmonic oscillator. Inner projection with perturbation theory yields rational approximations to Brillouin–Wigner-type perturbation expansions. These lower bounds are compared with [N ? 1, N] Padé approximants to the Rayleigh–Schrödinger perturbation series for this problem. These Padés are also expressible as the even convergents, w_2N, of a Stieltjes-type continued fraction. The latter representation has certain advantages with respect to its Padé counterpart. Inner projection without perturbation theory provides significantly better results than the perturbative version. The application of inner projection techniques to a perturbed hydrogen atom is not straightforward. The usual problems associated with the continuum spectrum of hydrogen are present. By means of a nonunitary “tilting” transformation associated with the Lie group SO(4, 2), these problems may be bypassed. In the SO(4, 2)-reformulated eigenvalue problem, a reinterpretation of the basic variables, as developed by Silverstone and Moats, yields a new Hamiltonian that permits direct use of the inner projection method. This method has been applied to the ground state of the hydrogen atom in a magnetic field, using both four- and eight-dimensional basis manifolds. This represents the first application of inner projection to this problem.     

A novel hydrogen-bonding N-oxide–sulfonamide–nitro N—H…O synthon determining the architecture of benzenesulfonamide cocrystals

The structures of novel cocrystals of 4-nitropyridine N-oxide with benzenesulfonamide derivatives, namely, 4-nitrobenzenesulfonamide–4-nitropyridine N-oxide (1/1), C₅H₄N₂O₃·C₆H₆N₂O₄S, and 4-chlorobenzenesulfonamide–4-nitropyridine N-oxide (1/1), C₆H₆ClNO₂S·C₅H₄N₂O₃, are stabilized by N—H…O hydrogen bonds, with the sulfonamide group acting as a proton donor. The O atoms of the N-oxide and nitro groups are acceptors in these interactions. The latter is a double acceptor of bifurcated hydrogen bonds. Previous studies on similar crystal structures indicated competition between these functional groups in the formation of hydrogen bonds, with the priority being for the N-oxide group. In contrast, the present X-ray studies indicate the existence of a hydrogen-bonding synthon including N—H…O(N-oxide) and N—H…O(nitro) bridges. We present here a more detailed analysis of the N-oxide–sulfonamide–nitro N—H…O ternary complex with quantum theory computations and the Quantum Theory of Atoms in Molecules (QTAIM) approach. Both interactions are present in the crystals, but the O atom of the N-oxide group is found to be a more effective proton acceptor in hydrogen bonds, with an interaction energy about twice that of the nitro-group O atoms.     

Diethyl piperazine‐1,4‐diyldioxalate

The ethyl oxamate group, N–C(O)–C(O)–OEt, in the title compound, alternatively called diethyl N,N′:N,N′‐bis(ethylene)dioxamate, C₁₂H₁₈N₂O₆, can be considered as being composed of two singly bonded amide and ester functionalities. The ethyl oxamate group is not planar. The two carbonyl groups are almost perpendicular, with an oxalyl O=C—C=O torsion angle of −111.34 (17)°. The mol­ecule is located on an inversion centre. Infinite supramolecular tapes, propagating along the b axis, are formed through soft C—H⋯O interactions which form a centrosymmetric R(12) motif.     

Normal Coordinate Analysis in Cartesian Space I. Planar Symmetric Xn Molecules

Normal coordinate analysis of X_n type molecules can be carried out in the Cartesian space as well as in the internal space. Force constants in Cartesian coordinates for aromatic compounds belonging to D_nh group are calculated. The force constants of benzene are evaluated from vibrational frequencies both in the ground state and the ¹B_1u excited state. The calculated frequencies of planar carbon vibration of annulene of any N are tabulated. The normal coordinates derived from the calculation of 10-annulene are roughly the same of naphthalene derived more elaborated by Scherer. The normal modes in 10-annulene are indeed good approximations to the ones in naphthalene. This conclusion is valid for the other aromatic compounds.     

CNDO-MO calculation of NnFm molecules

The s-p separation model CNDO -MO method has been introduced and developed for both the open- and closed-shell systems since 1975. This method has two chief advantages over most of the other CNDO methods. (1) The ns and np bases of the same atom may be considered independent to infer different bonding behavior. (2) Pariser–Parr and Nishimoto–Mataga approximations are applied to the Coulombic repulsion integrals, which not only simplifies the calculation and saves computer time but also gives reliable computational results. A series of nitrogen fluoride molecules such as NF, NF₂, NF₃, cis-N₂F₂, trans-N₂F₂, and N₂F₂ have been selected for this MO calculation. In each case, both ionization potential and dipole moment were calculated. The results are closer to the observed values than those reported in other works.     

Theoretical Studies on the Asymmetric Baeyer–Villiger Oxidation Reaction of 4‐Phenylcyclohexanone with m‐Chloroperoxobenzoic Acid Catalyzed by Chiral Scandium(III)–N,N′‐Dioxide Complexes

The mechanism and enantioselectivity of the asymmetric Baeyer–Villiger oxidation reaction between 4‐phenylcyclohexanone and m‐chloroperoxobenzoic acid ( m ‐CPBA ) catalyzed by Sc^III–N,N′‐dioxide complexes were investigated theoretically. The calculations indicated that the first step, corresponding to the addition of m ‐CPBA to the carbonyl group of 4‐phenylcyclohexanone, is the rate‐determining step (RDS) for all the pathways studied. The activation barrier of the RDS for the uncatalyzed reaction was predicted to be 189.8 kJ mol^?1. The combination of an Sc^III–N,N′‐dioxide complex and the m ‐CBA molecule can construct a bifunctional catalyst in which the Lewis acidic Sc^III center activates the carbonyl group of 4‐phenylcyclohexanone while m ‐CBA transfers a proton, which lowers the activation barrier of the addition step (RDS) to 86.7 kJ mol^?1. The repulsion between the m‐chlorophenyl group of m ‐CPBA and the 2,4,6‐iPr₃C₆H₂ group of the N,N′‐dioxide ligand, as well as the steric hindrance between the phenyl group of 4‐phenylcyclohexanone and the amino acid skeleton of the N,N′‐dioxide ligand, play important roles in the control of the enantioselectivity.     

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.     

Saturated amine oxides: part 10. hydroacridines: part 32. linear 17O/13C and 13C/13C chemical shift correlations between saturated azaheterocyclic N‐methylamine N‐oxides,and the methiodides of their parent amines

Two kinds of good linear correlations were found between the chemical shifts of saturated six‐membered azaheterocyclic N‐methylamine N‐oxides and the chemical shifts of the methiodides of their parent amines. One of the correlations occurs between the ¹⁷O chemical shift of the N⁺―O^– oxygen in the N‐oxides and the ¹³C chemical shift of the N⁺―CH₃ methyl group analogously situated in the appropriate methiodide (r = 0.9778). This correlation enables unambiguous configuration assignment of the N⁺―O^– bond, even if the experimentally observed ¹⁷O chemical shift of only one N‐epimer is available, provided the ¹³C chemical shifts of both N⁺―CH₃ groups in the methiodide are known and assigned; furthermore, it can be used also for the estimation of ¹⁷O chemical shifts of the N⁺―O^– oxygens in N‐epimeric pairs of N‐oxides, for which observed ¹⁷O data hardly become available. The second correlation is observed between the ¹³C chemical shift of the N⁺―CH₃ methyl group in the N‐oxides and the ¹³C chemical shift of the N⁺―CH₃ methyl group analogously situated in the appropriate methiodide (r = 0.9785). It can be used for safe configuration assignment of the N⁺―CH₃ group and, indirectly, also of the N⁺―O^– bond in an amine N‐oxide, even if no ¹⁷O NMR data, and the ¹³C chemical shift of only one N‐epimer is available. Copyright © 2015 John Wiley & Sons, Ltd.     

Darstellung,Kristallstrukturen und Schwingungsspektren von trans‐[Pt(N3)4X2]2–, X = Cl,Br, I

Synthesis, Crystal Structures, and Vibrational Spectra of trans ‐[Pt(N₃)₄X₂]^2–, X = Cl, Br, I By oxidative addition to (n‐Bu₄N)₂[Pt(N₃)₄] with the elemental halogens in dichloromethane trans‐(n‐Bu₄N)₂[Pt(N₃)₄X₂], X = Cl, Br, I are formed. X‐ray structure determinations on single crystals of trans‐(Ph₄P)₂[Pt(N₃)₄Cl₂] (triclinic, space group P1, a = 10.352(1), b = 10.438(2), c = 11.890(2) Å, α = 91.808(12), β = 100.676(12), γ = 113.980(10)°, Z = 1), trans‐(Ph₄P)₂[Pt(N₃)₄Br₂] (triclinic, space group P1, a = 10.336(1), b = 10.536(1), c = 12.119(2) Å, α = 91.762(12), β = 101.135(12), γ = 112.867(10)°, Z = 1) and trans‐(Ph₄P)₂[Pt(N₃)₄I₂] (triclinic, space group P1, a = 10.186(2), b = 10.506(2), c = 12.219(2) Å, α = 91.847(16), β = 101.385(14), γ = 111.965(18)°, Z = 1) reveal, that the compounds crystallize isotypically with octahedral centrosymmetric complex anions. The bond lengths are Pt–Cl = 2.324, Pt–Br = 2.472, Pt–I = 2.619 and Pt–N = 2.052–2.122 Å. The approximate linear Azidoligands with N^α–N^β–N^γ‐angles = 172.1–176.8° are bonded with Pt–N^α–N^β‐angles = 116.2–121.9°. In the vibrational spectra the platinum halogen stretching vibrations of trans‐(n‐Bu₄N)₂[Pt(N₃)₄X₂] are observed in the range of 327–337 (X = Cl), at 202 (Br) and in the range of 145–165 cm^–1 (I), respectively. The platinum azide stretching modes of the three complex salts are in the range of 401–421 cm^–1. Based on the molecular parameters of the X‐ray determinations the IR and Raman spectra are assigned by normal coordinate analysis. The valence force constants are f_d(PtCl) = 1.90, f_d(PtBr) = 1.64, f_d(PtI) = 1.22, f_d(PtN^α) = 2.20–2.27 and f_d(N^αN^β, N^βN^γ) = 12.44 mdyn/Å.     

On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

Charge‐transfer complexes of N‐methyl‐and N‐ethyl­carbazole with 3,5‐di­nitro­benzo­nitrile

In the two title compounds, N‐methyl­carba­zole–3,5‐di­nitro­benzo­nitrile (1/1), C₁₃H₁₁N·C₇H₃N₃O₄, (I), and N‐ethyl­carba­zole–3,5‐di­nitro­benzo­nitrile (1/1), C₁₄H₁₃N·C₇H₃N₃O₄, (II), the donor and acceptor mol­ecules are stacked alternately to form one‐dimensional columns. In (I), the N‐methyl group of the donor is nearly eclipsed with respect to one of the nitro groups of the neighboring acceptor in a column, whereas the N‐ethyl group is anti with respect to the cyano group of the neighboring acceptor in (II).     

Synthesis and characterization of organosoluble polyimides with trifluoromethyl‐substituted benzene in the side chain

New aromatic diamines substituted with a trifluoromethyl group in the side chain, 2,4‐diamino‐3′‐trifluoromethylazobenzene, 2,4‐diamino‐1‐[(4′‐trifluoromethylphenoxy) phenyl] aniline, and 3,5‐diamino‐1‐[(4′‐trifluoromethyl phenoxy) phenyl] benzamide were synthesized and characterized and used to prepare polyimides by a one‐step high‐temperature polycondensation method. Experimental results indicated that the prepared polyimides possess good solubility in strong organic solvents such as N‐methyl‐2‐pyrrolidinone, N,N′‐dimethylformamide, and N,N′‐dimethylacetamide. Homogeneous solutions with solid contents as high as 15–20% can be prepared, which are stable for storing longer than 2 weeks at room temperature. The polyimides exhibited glass‐transition temperatures of 249–292 °C and good thermal stability. The PI‐I_c and PI‐III_c films prepared by casting the fully imidized polymer solutions showed good transparency with cutoff wavelengths at 320–330 nm. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1572–1582, 2002     

Darstellung,Kristallstrukturen und Schwingungsspektren von trans‐[Pt(N3)4(ECN)2]2–, E = S,Se

Synthesis, Crystal Structures, and Vibrational Spectra of trans ‐[Pt(N₃)₄(ECN)₂]^2–, E = S, Se By oxidative addition to (n‐Bu₄N)₂[Pt(N₃)₄] with dirhodane in dichloromethane trans‐(n‐Bu₄N)₂[Pt(N₃)₄(SCN)₂] and by ligand exchange of trans(n‐Bu₄N)₂[Pt(N₃)₄I₂] with Pb(SeCN)₂ trans‐(n‐Bu₄N)₂[Pt(N₃)₄(SeCN)₂] are formed. X‐ray structure determinations on single crystals of trans‐(Ph₄P)₂[Pt(N₃)₄(SCN)₂] (triclinic, space group P 1, a = 10.309(3), b = 11.228(2), c = 11.967(2) Å, α = 87.267(13), β = 75.809(16), γ = 65.312(17)°, Z = 1) and trans‐(Ph₄P)₂[Pt(N₃)₄(SeCN)₂] (triclinic, space group P 1, a = 9.1620(10), b = 10.8520(10), c = 12.455(2) Å, α = 90.817(10), β = 102.172(10), γ = 92.994(9)°, Z = 1) reveal, that the compounds crystallize isotypically with octahedral centrosymmetric complex anions. The bond lengths are Pt–S = 2.337, Pt–Se = 2.490 and Pt–N = 2.083 (S), 2.053 Å (Se). The approximate linear Azidoligands with N^α–N^β–N^γ‐angles = 172,1–175,0° are bonded with Pt–N^α–N^β‐angles = 116,7–120,5°. In the vibrational spectra the platinum chalcogen stretching vibrations of trans‐(n‐Bu₄N)₂[Pt(N₃)₄(ECN)₂] are observed at 296 (E = S) and in the range of 186–203 cm^–1 (Se). The platinum azide stretching modes of the complex salts are in the range of 402–425 cm^–1. Based on the molecular parameters of the X‐ray determinations the IR and Raman spectra are assigned by normal coordinate analysis. The valence force constants are f_d(PtS) = 1.64, f_d(PtSe) = 1.36, f_d(PtN^α) = 2.33 (S), 2.40 (Se) and f_d(N^αN^β, N^βN^γ) = 12.43 (S), 12.40 mdyn/Å (Se).     

3‐Cyano‐6‐hydroxy‐4‐methyl‐2‐pyridone: two new pseudopolymorphs and two cocrystals with products of an in situ nucleophilic aromatic substitution

Four crystal structures of 3‐cyano‐6‐hydroxy‐4‐methyl‐2‐pyridone (CMP), viz. the dimethyl sulfoxide monosolvate, C₇H₆N₂O₂·C₂H₆OS, (1), the N,N‐dimethylacetamide monosolvate, C₇H₆N₂O₂·C₄H₉NO, (2), a cocrystal with 2‐amino‐4‐dimethylamino‐6‐methylpyrimidine (as the salt 2‐amino‐4‐dimethylamino‐6‐methylpyrimidin‐1‐ium 5‐cyano‐4‐methyl‐6‐oxo‐1,6‐dihydropyridin‐2‐olate), C₇H₁₃N₄⁺·C₇H₅N₂O₂⁻, (3), and a cocrystal with N,N‐dimethylacetamide and 4,6‐diamino‐2‐dimethylamino‐1,3,5‐triazine [as the solvated salt 2,6‐diamino‐4‐dimethylamino‐1,3,5‐triazin‐1‐ium 5‐cyano‐4‐methyl‐6‐oxo‐1,6‐dihydropyridin‐2‐olate–N,N‐dimethylacetamide (1/1)], C₅H₁₁N₆⁺·C₇H₅N₂O₂⁻·C₄H₉NO, (4), are reported. Solvates (1) and (2) both contain the hydroxy group in a para position with respect to the cyano group of CMP, acting as a hydrogen‐bond donor and leading to rather similar packing motifs. In cocrystals (3) and (4), hydrolysis of the solvent molecules occurs and an in situ nucleophilic aromatic substitution of a Cl atom with a dimethylamino group has taken place. Within all four structures, an R₂²(8) N—H...O hydrogen‐bonding pattern is observed, connecting the CMP molecules, but the pattern differs depending on which O atom participates in the motif, either the ortho or para O atom with respect to the cyano group. Solvents and coformers are attached to these arrangements via single‐point O—H...O interactions in (1) and (2) or by additional R₄⁴(16) hydrogen‐bonding patterns in (3) and (4). Since the in situ nucleophilic aromatic substitution of the coformers occurs, the possible Watson–Crick C–G base‐pair‐like arrangement is inhibited, yet the cyano group of the CMP molecules participates in hydrogen bonds with their coformers, influencing the crystal packing to form chains.     

Characterization of N‐methylated amino acids by GC‐MS after ethyl chloroformate derivatization

Methylation is an essential metabolic process in the biological systems, and it is significant for several biological reactions in living organisms. Methylated compounds are known to be involved in most of the bodily functions, and some of them serve as biomarkers. Theoretically, all α‐amino acids can be methylated, and it is possible to encounter them in most animal/plant samples. But the analytical data, especially the mass spectral data, are available only for a few of the methylated amino acids. Thus, it is essential to generate mass spectral data and to develop mass spectrometry methods for the identification of all possible methylated amino acids for future metabolomic studies. In this study, all N‐methyl and N,N‐dimethyl amino acids were synthesized by the methylation of α‐amino acids and characterized by a GC‐MS method. The methylated amino acids were derivatized with ethyl chloroformate and analyzed by GC‐MS under EI and methane/CI conditions. The EI mass spectra of ethyl chloroformate derivatives of N‐methyl ( 1–18 ) and N,N‐dimethyl amino acids ( 19–35 ) showed abundant [M‐COOC₂H₅]⁺ ions. The fragment ions due to loss of C₂H₄, CO₂, (CO₂ + C₂H₄) from [M‐COOC₂H₅]⁺ were of structure indicative for 1–18 . The EI spectra of 19–35 showed less number of fragment ions when compared with those of 1–18 . The side chain group (R) caused specific fragment ions characteristic to its structure. The methane/CI spectra of the studied compounds showed [M + H]⁺ ions to substantiate their molecular weights. The detected EI fragment ions were characteristic of the structure that made easy identification of the studied compounds, including isomeric/isobaric compounds. Fragmentation patterns of the studied compounds ( 1–35 ) were confirmed by high‐resolution mass spectra data and further substantiated by the data obtained from ¹³C₂‐labeled glycines and N‐ethoxycarbonyl methoxy esters. The method was applied to human plasma samples for the identification of amino acids and methylated amino acids. Copyright © 2016 John Wiley & Sons, Ltd.     

Indexing scheme for classes of 𝒮N; partitions of N

The classes of the symmetric group 𝒮_N are identified by partitions of N. In this work an indexing scheme is presented which provides a dense enumeration of the classes of 𝒮_N. The method is based on a graphical representation of partitions of N, which also enables the determination of the class corresponding to a given number. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 421–426, 1997     

β-Funktionalisierte Hydrazine aus N-Phthalimidoaziridinen und ihre hydrogenolytische N,N-Spaltung zu Aminen

β-Functionalized Hydrazines from N-Phthalimidoaziridines and their Hydrogenolytic N,N-Cleavage to Amines The three N-phthalimido-aziridines 1–3 were reacted with phenol, thiophenol, aniline, p-toluenesulfonic acid, and H₂O in selected combinations. These nucleophiles opened the 3-membered ring to yield the N-phthalimidoamines 4a–d, 5a–d, 6a–c , and 6e ; all these products (except the carbinol 6e ) carry an aryl-substituted functional group on the C-atom vicinal to the N-substituent. Hydrazinolysis of 4, 5, 6a–c , and 6e afforded the β-functionalized hydrazines 7, 8, 9a–c , and 9e . The reducing medium Raney-Ni/N₂H₄ transformed 4, 5, 6a–c , and 6e to the β-functionalized amines 10, 11, 12a–c , and 12e . By a study with the hydrazide 6a and the hydrazine 9a , it was shown that the N,N-cleavage is a catalytic hydrogenolysis by H₂ generated from N₂H₄ with Raney-Ni and that it does not take place on the hydrazide 6 , but rather on the hydrazine 9 , generated as intermediate from 6 with N₂H₄. Spectroscopic data confirmed that the conversions of 1–3 to 4–6 occurred exclusively with inversion and that the resulting configurations remained fully intact during the transformations of 4, 5 , and 6 (via 7, 8 , and 9 ) to 10, 11 , and 12 , respectively.     

Ortho effects in organic molecules on electron impact. 14—Concerted and stepwise ejections of SO2 and N2 from N-arylidene 2-nitrobenzenesulphenamides

Unexpected ortho interaction of the nitro group has been noticed during the mass spectral fragmentations of N-arylidene 2-nitrobenzenesulphenamides, where the molecular ions expel SO₂ and N₂ both in concerted and stepwise processes. Loss of a hydrogen or the substituent from this fragment leads to a very abundant ion in all the compounds studied. Based on chemical evidence and linked-scan studies, a 1,2-phenylenetropylium cation structure has been postulated for the [M–SO₂–N₂–H/substituent]⁺ ion.