Hydrogen bond studies: 80. A deuteron magnetic resonance and infrared spectroscopic study of the water molecule in lithium formate monohydrate,LiHCOO · H2O

A deuteron magnetic resonance and infrared study of the water molecules in lithium formate monohydrate, LiHCOO · H₂O, has been made. The quadrupole coupling constants (e²qQ/h) and asymmetry parameters (η) were found to be 198.7±0.4 and 231.3±0.6 kHz, and 0.060±0.005 and 0.097±0.003, respectively, at 25 ° C.An interpretation is given of the infrared spectra in the OH-stretching region in terms of intra- and intermolecular couplings of the water molecules. It is found that the water molecules are vibrationally distorted by their environments such that the OH-stretching modes consist of independent stretchings of the two O-H bonds.     

Path integrals on finite sets

We construct an analogue of the Feynman path integral for the case of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% aaaeaacaaIXaaabaGaamyAaaaadaWcaaqaaiabgkGi2cqaaiabgkGi% 2kaadshaaaqeduuDJXwAKbYu51MyVXgaiuaacqWFvpGAcaWG0bGaey% ypa0JaamisamaaBaaaleaacaGGOaaabeaakmaaBaaaleaacaGGPaaa% beaakiab-v9aQjaadshaaaa!4A8D!\[ - \frac{1}{i}\frac{\partial }{{\partial t}}\varphi t = H_( _) \varphi t\] in which H ₍₎ is a self-adjoint operator in the space L ²(M)= % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSOaHmkaaa!3744!\[\mathbb{C}\], where _M is a finite set, the paths being functions of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSyhHekaaa!375D!\[\mathbb{R}\] with values in M. The path integral is a family of measures F _t,t with values in the operators on L ²(M), or equivalently, a family of complex measures corresponding to matrix coefficients.It is shown that these measures on path space are in some sense dominated by the measure of a Markov process. This implies that F _t,t is concentrated on the set of step functions S[t,t].This allows one to make sense of, and prove, the analogue of Feynman's formula for the propagator of the Hamiltonian H=H ₀+V, where V is a potential, namely the formula: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyzamaaCa% aaleqabaGaeyOeI0IaamyAaiaacIcacaWG0bGaai4jaiabgkHiTiaa% dshacaGGPaGaamisaaaakiabg2da9maapebabaGaaeyzamaaCaaale% qabaGaeyOeI0IaamyAamaapedabaGaamOvaiaacIcatCvAUfKttLea% ryqr1ngBPrgaiuGacqWF4baEcaGGOaGaam4CaiaacMcacaGGPaGaae% izaiaabohaaWqaaiaadshaaeaacaWG0bGaai4jaaGdcqGHRiI8aaaa% kiaadAeadaWgaaWcbaGaamiDaiaacEcacaGGSaGaamiDaaqabaGcca% GGOaGaaeizaiab-Hha4jaacMcaaSqaaiaadofacaGGBbGaamiDaiaa% cYcacaWG0bGaai4jaiaac2faaeqaniabgUIiYdaaaa!6410!\[{\text{e}}^{ - i(t' - t)H} = \int_{S[t,t']} {{\text{e}}^{ - i\int_t^{t'} {V(x(s)){\text{ds}}} } F_{t',t} ({\text{d}}x)} \]and the corresponding formulas for the matrix coefficients, in which the integral extends over the paths beginning and ending in the appropriate points. We show that the measures F _t,t are completely determined by these equations and by a certain multiplicative property.The path integral corresponding to a two-particle system without interaction is the direct product of the corresponding path integrals. The propagator for a two-particle system with interaction can be obtained by repeated integration.Finally, we show that the above integral formula can be generalized to the case where the potential is time dependent.     

Analysis of Open Discrete Time Queueing Networks: A Refined Decomposition Approach

This paper deals with approximate analysis methods for open queueing networks. External and internal flows from and to the nodes are characterized by renewal processes with discrete time distributions of their interarrival times. Stationary distributions of the waiting time, the queue size and the interdeparture times are obtained using efficient discrete time algorithms for single server (GI/G/1) and multi-server (GI/D/c) nodes with deterministic service. The network analysis is extended to semi-Markovian representations of each flow among the nodes, which include parameters of the autocorrelation function.     

Thioacetylacetone: structural and vibrational assignments.

Thioacetylacetone and its variously deuterated isotopomers have been investigated using electronic and vibrational spectroscopy combined with quantum chemical calculations. Thioacetylacetone is known for its photochromic properties, but the structures of the initial and final forms have been the subject of a long debate. Analysis of the IR spectra recorded in low-temperature argon and xenon matrices, room-temperature solutions, and in the gas phase has allowed us to establish the nature of the photochromic species and of its precursor. Similar to the case of another beta-thioxoketone, monothiodibenzoylmethane, the photo-product has been assigned to the nonchelated SH exo-rotamer of the (Z)-enethiol tautomeric form, whereas the dominant ground-state species corresponds to the chelated (Z)-enol tautomeric form. Detailed vibrational assignments have been proposed for both forms based on quantum chemical calculations and polarization experiments. In the case of the chelated (Z)-enol species prevailing in the ground state, a second-order perturbative anharmonic analysis at the B3LYP/cc-pVTZ level indicated strong anharmonic effects associated with the intramolecular hydrogen bond, leading to a shift of more than 600 cm-1 of the wavenumber of the OH-stretching vibration. A small fraction of the SH endo-rotameric chelated (Z)-enethiol form was also detected under unperturbed conditions. The (Z)-enethiol form can be converted into the (Z)-enol form by irradiation at 290 nm.     

Transannular reactions of two parallel 1,3-butadiynes: syntheses,structures, and reactions of 1-azacyclotetradeca-3,5,10,12-tetrayne derivatives

The synthesis of 1-alkyl and 1-aryl-1-azacyclotetradeca-3,5,10,12-tetraynes was achieved in a stepwise approach. The key intermediate was 1,13-dibromotrideca-2,4,9,11-tetrayne (18). Reaction with methyl- (19 a), ethyl- (19 b), isopropyl- (19 c), n-butyl- (19 d), and tert-butylamine (19 e) as well as aniline (19 f) and p-methoxyaniline (19 g) gave the corresponding 14-membered tetraynes 20 a-20 g. The ring inversion process of 20 b was studied by variable temperature (1)H NMR spectroscopy. From these measurements a value of 10.6 kcal mol(-1) was calculated for DeltaG(not equal). X-ray investigations on single crystals of 20 b, 20 c, and 20 f revealed the axial position for the substituent at each nitrogen atom. For 20 b we encountered the chair conformation, for 20 c both chair and boat conformations, and for 20 f the boat conformation in the solid state. The reaction of 20 c with concentrated HCl in ethanol yielded 2,10-dichloro-6-isopropyl-6-azatricyclo[9.3.0.0(4,8)]tetradeca-1(11),2,4(8),9-tetraene (25 c). Compound 25 c was oxidized by 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) to 27 c. The structure of the latter was confirmed by X-ray investigations. The reaction of 20 c in aqueous HCl lead to the formation of 10-chloro-2-isopropyl-1,3,4,6,7,8-hexahydro-2H-benzo[g]isoquinolin-9-one (37 c). The structure of 37 c was verified by X-ray studies on single crystals.     

Synthesis of <Emphasis Type="Italic">N</Emphasis>-1-(Indanyloxymethyl) and <Emphasis Type="Italic">N</Emphasis>-1-(4-Hydroxybut-2-enyloxymethyl) Analogues of the HIV Drugs Emivirine and GCA-186

Summary. A series of Emivirine and GCA-186 analogues substituted at N-1 with indan-1-yloxymethyl (6a–6c) and indan-2-yloxymethyl (6d–6f) were synthesized by reaction of the corresponding bis(indanyloxy)methans with uracils having 5-ethyl or 5-isopropyl and 6-benzyl or 6-(3,5-dimethylbenzyl) substituents. A route to the corresponding N-1 substituted 4-hydroxybut-2-enyloxymethyl analogue was also devised. All newly synthesized compounds showed potent activity against wild-type HIV-1, the most active compound being 5-ethyl-1-(indan-1-yloxymethyl)-6-(3,5-dimethylbenzyl)uracil (6b), which was 50-fold more active than Emivirine.Present address: Chemistry Department, Faculty of Science, Tanta University, Tanta, EgyptA research center funded by The Danish National Research Foundation for studies on nucleic acid chemical biology     

The application of "click chemistry" for the decoration of 2(1H)-pyrazinone scaffold: generation of templates

The "click chemistry" approach has been explored on the 2-(1H)-pyrazinone scaffold for the generation of pharmacologically interesting heterocyclic moieties. Huisgen 1,3-dipolar cycloaddition has been evaluated as the key step for the construction of the 1,2,3-triazole ring at the C-3 position of 2-(1H)-pyrazinones. Two different pathways have been successfully evaluated: (1) via C-C or C-O linkage of the acetylenic part to the C-3 position of the 2-(1H)-pyrazinone scaffold or (2) via azide introduction in the C-3 position. The subsequent application of "click chemistry" resulted in the formation of hitherto unknown skeletons. Microwave irradiation has successfully been applied in different steps of the sequence.     

Note on a theoretical interpretation of the isotopic ratio vOH/vOD versus vOH in isotopically diluted HDO molecules in solid hydrates

A simple intra- and inter-molecular potential for water molecules engaged in hydrogen bonding has been used in a one-dimensional approximation for a theoretical interpretation of the experimental correlation $\text{v}$_OH/$\text{v}$_OD versus $\text{v}$_OH in solid hydrates. The variation in the equilibrium OH(D) distance has also been considered.