Ab initio study on NH+: Transition dipole moments,transition probabilities,and radiative lifetimes

The transition electric dipole moments between low-lying valence states of NH⁺ are calculated by an ab initio effective valence-shell Hamiltonian (H^v) method. The H^v calculated transition moments are found to be in good agreement with those by other accurate ab initio methods. The spontaneous emission probabilities for the A²− → X²Π, B²Δ → X²Π, and C²−⁺ → X²Π transitions of NH⁺ are computed. Also, radiative lifetimes for A²∑⁻, B²Δ, and C²∑⁺ states are all theoretically determined using the potential energy functions by H^v. Also, the H^v results are well compared with those computed using the Morse potentials and the rkr potentials which are obtained from experimental data. © 1996 John Wiley & Sons, Inc.     

TL glow-curve deconvolution functions for various kinetic orders and continuous trap distribution: Acceptance criteria for E and s values

The glow curve deconvolution (GCD) analysis of a composite thermoluminescence (TL) glow curve into its individual glow-peaks needs appropriate equations describing a single glow peak. In the present work, new single glow peak equations are presented, which are produced by transformation of the I(n ₀,E,s,T) and I(n ₀,E,s,b,T) single glow-peak equations into I(I _m,T _m,E,T) and I(I _m,T _m,E,b,T), respectively. Moreover, equations of the forms I(I _m,T _m,w,b,T) are also introduced. The proposed equations have two basic advantages: (1) they use parameters, which are directly obtained from the experimental glow peaks and (2) their accuracy is equal to that of the original thermoluminescence single glow-peak equations.     

Crosslinked polymer chains with excluded volume: A new class of branched polymers?

In this note microgels with and without excluded volume interactions are considered. Based on earlier exact computations on Gaussian mircogels, which are formed by self-crosslinking (with M crosslinks) of polymer chains with chainlength N, Flory type approximations are used to get first insight to their behavior in solution. It is shown that two different types of microgels exist: A special type of branched polymer whose size scales as R ∝ N^2/5/M^−1/5, instead of R ∝ N^1/2. The second type are c^*-microgels whose average mesh sizes r are swollen and form self avoiding walks with a scaling law of the form r = a(N/M)^3/5.     

STEREOELECTRONIC PROPERTIES OF PHOTOSYNTHETIC AND RELATED SYSTEMS — V. AB INITIO CONFIGURATION INTERACTION CALCULATIONS ON THE GROUND AND LOWER EXCITED SINGLET AND TRIPLET STATES OF ETHYL CHLOROPHYLLIDE a AND ETHYL PHEOPHORBIDE a

Abstract— Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying excited singlet and triplet states of ethyl pheophorbide a (Et-Pheo a) and ethyl chlorophyllide a (Et-Chl a), and are employed in an analysis of the electronic absorption spectra of these systems. In both molecules the visible spectrum is found to consist of transitions to the two lowest-lying ¹(π, π*) states, S₁ and S₂. The configurational compositions of S₁ and S₂ in both molecules are similar, and are described qualitatively in terms of a four-orbital model. The S₁← S₀ transition in each case is predicted to be intense, and is largely in-plane y-polarized, while the S₂← S₀ transition is predicted to be extremely weak and in-plane polarized. The orientation of the S₂← S₀ transition dipole is not conclusively established in the present calculations. The Soret band in both molecules is composed of transitions to no less than ten states (S_3-S₁₂ in Et-Chl a and S₃-S₇S₉-S₁₂. and S₁₄ in Et-Pheo a), which exhibit primarily (π, π*) character. The configurational compositions of these states are generally a complex mixture of excitations from both occupied macrocyclic π molecular orbitals and occupied orbitals with electron density in the cyclopen-tanone ring and the carbomethoxy chain. No clear correspondences are evident between respective Soret states of the two systems. Transitions to these states are generally intense and display a variety of in-plane polarizations. Two additional Soret states of Et-Pheo a, S₈ and S₁₃, exhibit primarily (n. π*) character. S₈ is characterized by excitations from u and non-bonding regions of the carbomethoxy chain, while S₁₃ is described by n →π* excitations involving the nitrogen atom of ring II. No corresponding (n, π*) states were found for Et-Chl a. In both molecules the lowest two triplet states, T₁ and T₂, are found to lie lower in energy than S₁. while T, and S₁ are approximately degenerate. The configurational compositions of T₁-T₄ of both molecules are nearly identical, and may be described by a four-orbital model. However, the compositions of T₁-T₄ differ sharply from those of S₁ and S₂. A number of higher-lying ³(π, π*) states of both molecules (T₅-T₁₃ in Et-Chi a and T₈-T₉, T₁₁-T₁₃ in Et-Pheo a) are found to have energies similar to the singlet Soret states, relative to S₀. They are characterized by a complex mixture of configurations which do not include significant contributions involving the four-orbital model. In addition, two ³(n, π*) states of Et-Pheo a, T₁₀ and T₁₄, are found, which are somewhat analogous to S₈ and S₁₃. Additional data presented include the charge distributions and molecular dipole moments of the S₀. S₁, and T₁ states of both molecules, as well as energies and oscillator strengths of computed S_n←S₁ and T_n←₁ transitions.     

A new type of piezoelectric detector in liquid: Part 2. Computation of the equivalent circuit parameters of a piezoelectric crystal with a separated electrode and of series piezoelectric sensors in a non-electrolyte solution

An improved equivalent circuit model is proposed for a piezoelectric crystal with a separated electrode. Equations are derived for the equivalent circuit parameters in a non-electrolyte solution and are verified experimentally. The resonance frequency f_s is given by f_s = f₀[1 + C₁/2(C′₀ + C_s)], where f₀, C₁ and C′₀ are the resonance frequency, motional capacitance and the shunt capacitance of the crystal respectively and C_s is the solution capacitance. The mechanical quality factor is the same as that of the crystal. The motional resistance, motional inductance, motional capacitance and shunt capacitance are respectively K², K², K⁻² and K⁻¹ times those of the crystal, where K = 1 + C′₀/C_s. The influence of the permittivity, density and viscosity of the solution and the configuration of the sensors on the equivalent parameters are investigated. The equivalent circuit parameters of a series piezoelectric crystal are also calculated and measured.     

Pressure Effects in the Solvolysis of Benzyl Chlorides

Rates of solvolysis of benzyl chloride and of substituted benzyl chlorides have been measured in an acetone-water mixture (acetone mole fraction 0.147) at pressures ranging from atmospheric to 1 kbar. Pressure studies have also been made for p-methyl benzyl chloride in various acetone-water mixtures. Measurements have also been made of the partial molar volumes of the reactants. The plots of log k against pressure are fitted to a second-degree polynomial in P, and values of ΔV^? and (δΔV^//δP)_T are obtained. The ΔV^? values are all negative, having values ranging from ?18 to ?24 cc/mole. The results are interpreted on the view that the mechanisms are S_N2(1), i.e. are towards the S_N1 end of the S_N2 spectrum of behavior. The ΔV^? values steadily become more negative in the series p? CH₃, H, p? Cl, pNO₂, and this is interpreted in terms of the greater spreading of positive charge in the p? CH₃ case and in terms of greater S_N2(2) character in the p? NO₂ case. The ΔV^? values go through a minimum as the solvent composition is varied, a result that is related to the existence of a corresponding maximum in the partial molar volumes of the reactant. The (δΔV^?/δP)_T values show a negative correlation with ΔV^?, suggesting, as expected, that the more compact activated complexes are the least compressible.     

On molecular topological properties of hex‐derived networks

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure–activity relationship/quantitative structure–property relationship study, physico‐chemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study hex‐derived networks HDN1(n) and HDN2(n), which are generated by hexagonal network of dimension n and derive analytical closed results of general Randić index R_α(G) for different values of α, for these networks of dimension n. We also compute the general first Zagreb, ABC, GA, ABC₄, and GA₅ indices for these hex‐derived networks for the first time and give closed formulae of these degree‐based indices for hex‐derived networks. Copyright © 2016 John Wiley & Sons, Ltd.     

Preparation and Characterization of New C2‐ and C1‐Symmetric Nitrogen,Oxygen, Phosphorous,and Sulfur Derivatives and Analogs of TADDOL. Part II

TADDOL (=α,α,α′,α′‐Tetraaryl‐1,3‐dioxolane‐4,5‐dimethanol) and the corresponding dichloride are converted to TADDAMINs (=(4S,5S)‐2,2,N,N′‐tetramethyl‐α,α,α′,α′‐tetraphenyl‐1,3‐dioxolan‐4,5‐dimethanamines) (Scheme 2) and ureas, 12 – 15 , and to TADDOP derivatives with seven‐membered O? P? O ester rings (Schemes 3 and 4). Cl/P‐Replacement via the Michaelis? Arbuzov reaction (Scheme 7) on mono‐ and dichlorides, derived from TADDOL, are described. It was not possible to obtain phosphines with the P‐atom attached to the benzhydrylic C‐atom of the TADDOL skeleton (Schemes 6 and 7). The X‐ray crystal structures (Figs. 1 and 2) of ten of the more than 30 new TADDOL derivatives are discussed. Full experimental details are presented.     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

Isobaric thermal behavior of glasses during uniform cooling and heating: Dependence of the characteristic temperatures on the relative contributions of temperature and structure to the rate of recovery. II. A one-parameter model approach

Isobaric variations of the characteristic temperatures T_g and T_max, obtained on uniform cooling and heating of glasses, are investigated in terms of their dependence on the relevant experimental variables, using a single retardation time model. The corresponding partial derivatives of T_g and T_max are derived as functions of the partition parameter x (ranging between zero and unity), which determines the relative contributions of temperature and structure to the retardation time. It is shown that the variation of T_g with the cooling rate is independent of x. In contrast, T_max critically depends on x, and its value as well as those of its three partial derivatives are linear functions of x^?1. The variations of T_max are analyzed in terms of a set of reduced variables, leading to simple reduction rules between any two of the experimental variables when the third is kept invariant. The reduction rules are further substantiated by investigating the behavior of glasses in two-step thermal cycles, which result in a unique set of inter-relationships between any pair of the partial derivatives of T_max, whatever the value of x. The results are discussed in terms of their relevance to the behavior of real glasses.     

Dirac equation with a Coulomb plus scalar potential in D + 1 dimensions

We generalize the Dirac equation to D + 1‐dimensional spacetime. The exact solutions of the D‐dimensional radial equations with a Coulomb plus scalar potential taking the form 1/r are analytically presented by studying the Tricomi equations. The energies E(n, l, D) are exactly presented. The dependences of the energies E(n, l, D) on the dimension D are analyzed in some detail. The energies E(n, 0, D) first decrease and then increase when increasing dimension D, but the energies E(n, l, D) (l ≠ 0) increase when increasing dimension D. The energies E(n, 0, D) are symmetric with respect to D = 1 for D ∈ (0, 2). It is shown that the energies E(n, l, D) (l ≠ 0) are almost independent of the quantum number l for large D and are completely independent of it if the Coulomb potential is equal to the scalar one. The energies E(n, l, D) almost overlap for large D. The dependences of the energies E(n, l, v) and E(n, l, s) on the vector potential parameter v and scalar potential one s are also studied for D = 3. All are found to decrease when these parameters are increased. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Complex coordinates and the Stark effect

The theories of the dilatation, r → r e^iθ, and translation, x → x + iq, transformations as related to the Stark problem are reviewed, and new results obtained. Results for the hydrogen atom n = 1 and n = 2 levels and the ¹P⁰, 2s2p H^? shape resonance in dc fields are presented, and the extension to the ac Stark effect made. Spectral estimates are made using the technique of the numerical range and via discussion of several model problems, using both coordinate rotation and coordinate translation.     

Inexpensive vibrational anharmonicities from estimated derivatives: Diatomic molecules

Four alternatives are compared for estimating vibrational anharmonicity constants without explicitly calculating the expensive fourth derivatives of the potential curves. In the first, semiempirical approach, fourth derivatives for 53 diatomic molecules are estimated from ab initio second and third derivatives by using the Morse model potential. Vibrational anharmonicities ω_ex_e are then computed from the third and fourth derivatives. The second approach invokes a purely empirical linear correlation between ω_ex_e and the harmonic frequencies ω_e. The third and fourth empirical approaches suppose that the effective harmonic and anharmonic force constants are proportional (with an additive constant in the fourth approach). Experimental values for ω_ex_e are compared with empirical predictions and with semiempirical estimates based upon Hartree–Fock (HF), Møller–Plesset (MP2), and local, nonlocal, and hybrid density-functional theories (DFT), using the small 6-31G* basis set. Ab initio values of ω_e and bond lengths r_e are also compared against experiment. The (U)MP2 results are the worst and include several anomalies. The other semiempirical methods yield results of comparable accuracy for ω_ex_e of hydrides, although the DFT methods are markedly better for ω_e and r_e and for ω_ex_e of nonhydrides. The empirical estimates are nearly as good as the semiempirical ones. We conclude that: (1) both empirical and semiempirical approximations are useful for predicting stretching anharmonicity constants ω_ex_e to precisions of σ≈5 cm⁻¹ for hydrides and σ≈1.5 cm⁻¹ for nonhydrides; and (2) MP2 theory is relatively unreliable for such calculations. In addition, we find the following tests to be useful when evaluating the reliability of vibrational constants calculated at the UMP2 level: (a) the calculated values of ω_e and ω_ex_e should not deviate substantially from the empirical relations; (b) harmonic frequencies and intensities calculated at the MP2 level should be smaller than those calculated at the corresponding HF level; (c) a large distance-dependence of the spin contamination, d〈S²〉/dR≳0.05 Å⁻¹, suggests that calculated constants are too large. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1315–1324, 1998     

Calculation of j and jm symbols for arbitrary compact groups. III. Application to SO3 ⊃ T ⊃ C3 ⊃ C1

The methodology developed in earlier papers is used to compute the 6j symbols and 3jm factors that arise in the group chain SO₃ ? T ? C₁. The relevant character theory is given and the 2j and 3j symbols calculated. Selection rules are used to predict which j symbols or jm factors are necessarily zero, and then a set of 6j fundamentals computed for T. The complete set of primitive 6j symbols are then computed by application of the orthogonality and Racah backcoupling relations. Primitive 3jm factors are calculated for SO₃ ? T and T ? C₃ and, from these, all the 3jm factors for T ? C₃ and some of those for SO₃ ? T computed. A complete table of non-equivalent 6j symbols for T and 3jm factors for T ? C₃ is given, together with a table for SO₃ ? T of all 3jm factors with j ≤ 2.     

Cycloaddition Reactions of 7‐Benzylidenecycloocta‐1,3,5‐triene with Ethenetetracarbonitrile and 4‐Phenyl‐3H‐1,2,4‐triazole‐3,5(4H)‐dione

An (E)/(Z) mixture (3 : 2) of 7‐benzylidenecycloocta‐1,3,5‐triene ( 5 ) is obtained when 1‐benzylcycloocta‐1,3,5,7‐tetraene ( 7 ), prepared by an improved procedure, is treated with t‐BuOK in THF. Alternatively, a ca. 9 : 1 mixture (E)/(Z)‐ 5 can be prepared in a Wittig reaction involving benzaldehyde and cycloocta‐2,4,6‐trien‐1‐ylidenetriphenylphoshorane ( 9 ). Treatment of (E)/(Z)‐ 5 88 : 12 with ethenetetracarbonitrile (TCNE) gave a complex mixture of products, from which seven mono‐adducts and two bis‐adducts were isolated (Sect. 2.2.1). Of the mono‐adducts, four are π4+π2 adducts: two ((E)‐ and (Z)‐isomers) are derived from valence tautomers of the two isomers of (E)/(Z)‐ 5 , while it is tentatively suggested that the other two (again (E)‐ and (Z)‐isomers) are formed from the intermediacy of a pentadienyl zwitterion (Sect. 2.3). The remaining three mono‐adducts, two of which are epimers, are π8+π2 adducts. It is suggested that they are derived from the intermediacy of homotropylium zwitterions (Sect. 2.3). For the two bis‐adducts, it is postulated that they are derived from an initial π2+π2 cycloaddition involving the homotropylium zwitterions followed by π4+π2 cycloaddition to the valence tautomer of each of the π2+π2 cycloadducts. With 4‐phenyl‐3H‐1,2,4‐triazole‐3,5(4H)‐dione ( 6 ), (E)/(Z)‐ 5 91 : 9 yielded two π4+π2 cycloadducts ((E)‐ and (Z)‐isomers) as well as two epimeric π8+π2 cycloadducts (Sect. 2.2.2). The intermediacy of pentadienyl (tentative suggestion) and homotropylium zwitterions accounts for the formation of the products (Sect. 2.3).     

Zum thermochemischen Verhalten von Halogeniden,Oxidhalogeniden, Aluminiumhalogeniden und Ammoniumhalogeniden der Seltenerdelemente

The Thermochemical Behaviour of Halides, Oxidehalides, Aluminiumhalides and Ammoniumhalides of Rare‐Earth‐Elements After a critical sifting of the thermal behaviour of Rare earth halides LnX₃, oxide halides LnOX, aluminium halides Ln_mAl_nX_3(m+n) and ammonium halides (NH₄)_xLn_yX_3y+x the enthalpies of formation and the standard entropies are evaluated and the recommended values are indicated. From the straight‐line dependence between the differences of the enthalpies of formation of Rare earth oxides and ‐halides as well as ‐oxidhalides and the ion radii of the concerned elements the values for some halides and oxide halides, which are missing in the literature, are deduced. The evaporation and sublimation behaviour of the LnX₃ as well as the decomposition behaviour of the compounds LnOX are generalizing described and chemical vapour transport properties of the LnX₃ with AlX₃ are systematically arranged. The thermal stability of the Europium trihalides is quantified. From the well known phase barograms and diagrams of the systems Rare earth trihalide/aluminium halide (LnX₃/AlX₃) and ammonium halide (LnX₃/NH₄X) general conclusions are deduced for systems with LnX₃.     

The effect of network architecture on the thermal and mechanical behavior of epoxy resins

The effects of crosslink functionality (f_c), molecular weight between crosslinks (M_c), and chain stiffness display on the thermal and mechanical behavior of epoxy networks are determined. Both f_c and M_c are controlled by blending different functionality amines with a difunctional epoxy resin. Chain stiffness is controlled by changing the chemical structure of the various amines. In agreement with rubber elasticity theory, the rubbery moduli are dependent on f_c and M_c, but independent of chain stiffness. The glassy moduli and secondary relaxations of these networks are relatively independent of f_c, M_c, and chain stiffness. However, the glass transition temperatures (T_g) of these networks are dependent on all three structural variables. This trend is consistent with free volume theory and entropic theories of T_g. f_c, M_c, and chain stiffness control the yield strength of these networks in a manner similar to that of T_g and is the result that both properties involve flow or relaxation processes. Fracture toughness, as measured by the critical stress intensity factor (K_Ic), revealed that f_c and M_c are both critical parameters. The fracture behavior is the result of the fracture toughness being controlled by the ability of the network to yield in front of the crack tip. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1371–1382, 1998     

Medium-size Gaussian basis sets for hydrogen through argon

Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the² P states of Li and Na, and the³ P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size.     

The theory of phase transition kinetics with growth site impingement. II. Heterogeneous nucleation

The kinetics of phase transformation are treated for heterogeneous nucleation, where all nuclei are simultaneously initiated, and where initiation follows first-order kinetcs. The phase transformation curves are sigmoid. For simultaneous initiation in two dimensions, a(t)/(1 ? a(t)) ∝ t². For first-order initiation, we have, approximately, a(t)/(1 ? a(t)) ∝ t^2.85, and v(t)/(1 ? v(t)) ∝ t^3.74.     

Diastereoselective Synthesis of Nitroaldol Derivatives

Three methods are described by which diastereomerically enriched nitroaldols and their O-silylated derivatives can be prepared. threo-Nitroaldols prevail up to 10:1 over the erythro-isomers if doubly deprotonated nitroaldols 28 are quenched with acetic acid (THF/HMPT or DMPU, ? 100°) (see Scheme 5 and Table 2). O-Trimethyl- or O-(t-butyl)dimethylsilylated (TBDMSi) erythro-nitroaldols can be obtained by protonation of the corresponding lithium nitronates ( 35, 39 ) in THF at low temperature (see Schemes 6 and 7). The erythro-O-TBDMSi-nitroaldol derivatives are also formed in the fluoride catalyzed addition of TBDMSi-nitronates ( 40–45 ) to aldehydes (see Schemes 8 and 9), In the latter reaction no 1,2-asymmetric induction is observed if a-branched silylnitronates or aldehydes are employed (see 48/49 and 50/51 ) – The stereochemical course of the reactions leading to erythro-O-TBDMSi-nitroaldols follows topological rules of broad applicability (see Scheme 10); possible mechnisms are discussed. - The configuration of diasteromerically ¹³C-NMR. Spectroscopy. – Some examples of the preparation of diastereimerically enriched 1,2-aminolcohols by reduction of the correspondence nitro compounds without loss of configurational purity are described (see Schemes 11 and 12).