Correlated holes and their relationships with reduced density matrices and cumulants

This paper describes a matrix formulation for the correlated hole theory within the framework of the domain-averaged model in many electron systems (atoms, molecules, condensed matter, etc.). General relationships between this quantity and one-particle reduced density matrices for any independent particle or correlated state functions are presented. This formulation turns out to be suitable for computational purposes due to the straightforward introduction of cumulants of two-particle reduced density matrices within the quantum field structure. Numerical calculations in selected simple molecular systems have been performed in order to determine preliminary correlated values for such a quantity.     

Passages through resonance in weakly nonlinear systems

A method of determining asymptotic expansions for weakly couplednonlinearly perturbed systems of harmonic oscillators with slowlyvarying frequencies is presented. In an example with two oscillators,each one experiences a separate resonance passage that producesa first-order amplitude change. Simultaneously, second-orderadjustments occur to both oscillators. The determination isachieved by carrying the calculations to third order.     

Addressing the Structural Complexity of Fluorinated Glucose Analogues: Insight into Lipophilicities and Solvation Effects

In this work, we synthesized all mono-, di-, and trifluorinated glucopyranose analogues at positions C-2, C-3, C-4, and C-6. This systematic investigation allowed us to perform direct comparison of ¹⁹F resonances of fluorinated glucose analogues and also to determine their lipophilicities. Compounds with a fluorine atom at C-6 are usually the most hydrophilic, whereas those with vicinal polyfluorinated motifs are the most lipophilic. Finally, the solvation energies of fluorinated glucose analogues were assessed for the first time by using density functional theory. This method allowed the log P prediction of fluoroglucose analogues, which was comparable to the C log P values obtained from various web-based programs.     

Single-crystal Raman spectroscopy and X-ray crystallography at beamline X26-C of the NSLS

Three-dimensional structures derived from X-ray diffraction of protein crystals provide a wealth of information. Features and interactions important for the function of macromolecules can be deduced and catalytic mechanisms postulated. Still, many questions can remain, for example regarding metal oxidation states and the interpretation of `mystery density', i.e. ambiguous or unknown features within the electron density maps, especially at ～2 ? resolutions typical of most macromolecular structures. Beamline X26-C at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL), provides researchers with the opportunity to not only determine the atomic structure of their samples but also to explore the electronic and vibrational characteristics of the sample before, during and after X-ray diffraction data collection. When samples are maintained under cryo-conditions, an opportunity to promote and follow photochemical reactions in situ as a function of X-ray exposure is also provided. Plans are in place to further expand the capabilities at beamline X26-C and to develop beamlines at NSLS-II, currently under construction at BNL, which will provide users access to a wide array of complementary spectroscopic methods in addition to high-quality X-ray diffraction data.     

Coupling to the pyrimido[4,5-b][1,4]oxazine ring system: Synthesis of potential antifolates

The ability of 2-amino-4-hydroxy-7H-pyrimido[4,5-b][1,4]oxazine derivatives to inhibit dihydrofolate reductase led to a search for means of synthesizing new side chain substituted analogs of this marginally stable pyrimidooxazine system. A study of the synthesis and use of 6-functionalized pyrimido[4,5-b][1,4]oxazines for coupling side chains was begun and has now revealed methods for coupling p-aminobenzoic acid with 2-amino-4-hydroxy-6-carboxy-7H-pyrimido[4,5-b][1,4]oxazine and hydrolyzed 2-amino-4-hydroxy-6-carbe-thoxymethylene-6,7-dihdyro-5H-pyrimido[4,5-b][1,4]oxazine. The products are of interest for evaluation as potential antifolates.     

J pulses for multiplet-selective NMR

Exact product operator solutions have been obtained for the evolution of weakly coupled spin-(1/2) I(m)S(n) systems during arbitrary RF irradiation of one spin. These solutions, which completely characterize the nature of J-coupling modulation during RF pulses, show that significant exchange occurs between single-spin magnetization and two-spin product operator states when the RF field strength is comparable to the coupling. In particular, a long (t(p) = [2J](-1) s), low-power (B(1) = J/2 Hz), constant amplitude pulse applied on resonance to one spin in an IS system completely interconverts the spinstates S(z) <--> 2S(x)I(z) and S(x) <--> 2S(z)I(z) when the RF is applied to the S spins, and interconverts S(x) <--> 2S(y)I(y) in 100% yield when the RF is applied to the I spins. Thus, these "J pulses," which select a bandwidth approximately equal to J Hz, may replace any combination of a (2J)(-1) delay period and a consecutive hard 90 degrees pulse in any polarization transfer or multiple quantum sequence. Although these rectangular pulses are highly frequency selective, in general they increase the replaced (2J)(-1) period by only a modest 40%, a time saving of a factor of 5 compared to existing pulses exhibiting the same selectivity. In favorable cases, there is no increase in duration of a pulse sequence using a particular type of J pulse, the 90(J) variety, which accomplishes the third spin state transformation listed above. J pulses will be advantageous for systems subject to rapid signal loss from relaxation and more generally for the enhanced operation of pulse sequences via the use of J modulation during RF irradiation.     

A Vector Model of Adiabatic Decoupling

A vector model of adiabatic decoupling is enunciated for an IS-coupled system of two spin- heteronuclei in the high-power limit of ideal adiabatic pulses. The observed S-spin magnetization evolves according to a time-dependent coupling that scales as thezcomponent of an I-spin vector which evolves due to the applied decoupling irradiation. Simple analytical expressions are derived both on and off resonance for the reduced coupling during an ideal sech/tanh inversion pulse and for the resulting signal when either in-phase or antiphase magnetization is present at the start of decoupling. The resulting model allows one to readily envision decoupling experiments, make accurate estimates of sideband intensity, and assess the relative performance of different decoupling schemes. The utility of the model is further demonstrated by applying it to several recently proposed methods for reducing sidebands. In the limit of ideal adiabatic pulses, the predictions of the vector model are almost identical to those of quantum mechanics. At the lower RF power levels used in practical adiabatic decoupling applications, where the pulses are no longer perfectly adiabatic, phase cycles are employed to achieve performance that approximates the ideal limits derived here, so the vector model is more generally applicable, as well. These limits establish standards for future determination of the most efficient parameters for practical applications of broadband adiabatic decoupling in a single transient.     

Functionalized and Partially or Differentially Bridged Resorcin[4]arene Cavitands: Synthesis and Solid‐State Structures

We report the synthesis and structural characterization of modified Cram‐type, resorcin[4]arene‐based cavitands. Two main loci on the cavitand backbone were selected for structural modification: the upper part (wall domain) and the lower part (legs). Synthesis of unsymmetrically bridged cavitands with different wall components (i.e., 7, 8 , and 14 – 18 ) was performed by stepwise bridging of the four couples of neighboring, H‐bonded OH‐groups of octol 1a (Schemes 1, 2, 4, and 5). Cavitands with modified legs (i.e., 20, 24, 27 , and 28 ), targeted for surface immobilization, were synthesized by short routes starting from suitable aldehyde starting materials incorporating either the fully preformed leg moieties or functional precursors to the final legs (Schemes 7–10). The new cavitand substitution patterns described in this paper should enable the construction of a wide variety of functional architectures in the future. X‐Ray crystallography afforded the characterization of cavitands 2c (Fig. 3) and 24 (Fig. 7) in the vase conformation, with 2c featuring a well‐ordered CH₂Cl₂ guest molecule in its cavity. A particular highlight is the X‐ray crystal‐structure determination of octanitro derivative 19 (Scheme 6), which, for the first time, shows a cavitand, lacking substituents in the ortho‐position to the two O‐atoms of the four resorcinol moieties, in the kite‐conformation (Fig. 5).     

Synthesis and reactions of 4,6-dimethoxyindole,an unusual indole system

A synthesis of 4,6-dimethoxyindole is described. Formylation or oxalylation reactions gave substitution at position 7 rather than the usual 3-substitution characteristic of other indoles. A synthesis of N,N-dimethyl-4,6-dimethoxytryptamine is presented along with NMR data for 3 and 7-substituted compounds in this series.