Application of main component fraction collection method for purification of compound libraries

In order to support high-throughput library purification, a novel UV triggered fraction collection method was developed in which a maximum-seeking-algorithm-driven, six-port valve collects the largest chromatographic peak. This straightforward strategy achieves the one sample-one fraction approach, thus resulting in a simpler and less error prone workup procedure. The effectiveness of this main component fraction collection method will be illustrated here by the results of the purification of compound libraries (altogether 6086 compounds, having an averaged success rate of 79.4%). Advanced applications, where the desired component differs from the main component, will also be discussed.     

Treating singularities present in the Sutcliffe-Tennyson vibrational Hamiltonian in orthogonal internal coordinates

Two methods are developed, when solving the related time-independent Schrodinger equation (TISE), to cope with the singular terms of the vibrational kinetic energy operator of a triatomic molecule given in orthogonal internal coordinates. The first method provides a mathematically correct treatment of all singular terms. The vibrational eigenfunctions are approximated by linear combinations of functions of a three-dimensional nondirect-product basis, where basis functions are formed by coupling Bessel-DVR functions, where DVR stands for discrete variable representation, depending on distance-type coordinates and Legendre polynomials depending on angle bending. In the second method one of the singular terms related to a distance-type coordinate, deemed to be unimportant for spectroscopic applications, is given no special treatment. Here the basis set is obtained by taking the direct product of a one-dimensional DVR basis with a two-dimensional nondirect-product basis, the latter formed by coupling Bessel-DVR functions and Legendre polynomials. With the basis functions defined, matrix representations of the TISE are set up and solved numerically to obtain the vibrational energy levels of H3+. The numerical calculations show that the first method treating all singularities is computationally inefficient, while the second method treating properly only the singularities having physical importance is quite efficient.     

A study of structural and bonding variations in the homologous series [Mo(2)(CN)(6)(dppm)(2)](n-) (n = 2, 1, 0)

Reaction of Mo(2)Cl(4)(dppm)(2) (dppm = bis(diphenylphosphino)methane) with 6 equiv of [n-Bu(4)N][CN] or [Et(4)N][CN] in dichloromethane yields [n-Bu(4)N](2)[Mo(2)(CN)(6)(dppm)(2)] (1) and [Et(4)N](2)[Mo(2)(CN)(6)(dppm)(2)] (2), respectively. The corresponding one- and two-electron oxidation products [n-Bu(4)N][Mo(2)(CN)(6)(dppm)(2)] (3) and Mo(2)(CN)(6)(dppm)(2) (4)were prepared by reactions of 1 with the oxidant NOBF(4). Single-crystal X-ray structures of 2.2CH(3)CN, 3.2CH(3)CN.2H(2)O, and 4.2CH(3)NO(2) were performed, and the results confirmed that all three complexes contain identical ligand sets with trans dppm ligands bisecting the Mo(2)(mu-CN)(2)(CN)(4) equatorial plane. The binding of the bridging cyanide ligands is affected by the oxidation state of the dimolybdenum core as evidenced by an increase in side-on pi-bonding overlap of the mu-CN in going from 1 to 4. The greater extent of pi-donation into Mo orbitals is accompanied by a lengthening of the Mo-Mo distance (2.736(1) A in Mo(2)(II,II) (2), 2.830(1) A in Mo(2)(II,III) (3), and 2.936(1) A in Mo(2)(III,III) (4)). A computational study of the closed-shell members of this homologous series, [Mo(2)(CN)(6)(dppm)(2)](n)() (n = 2-, 0), indicates that the more pronounced side-on pi-donation evident in the X-ray structure of 4 leads to significant destabilization of the delta orbital and marginal stabilization of the delta() orbitals with respect to nearly degenerate delta and delta orbitals in the parent compound, 2. The loss of delta contributions combined with the reduced orbital overlap due to higher charges on molybdenum centers in oxidized complexes 3 and 4 is responsible for the observed increase in the length of the Mo-Mo bond.     

Ab initio torsional potential and transition frequencies of acetaldehyde

High-level ab initio electronic structure calculations, including extrapolations to the complete basis set limit as well as relativistic and diagonal Born-Oppenheimer corrections, resulted in a torsional potential of acetaldehyde in its electronic ground state. This benchmark-quality potential fully reflects the symmetry and internal rotation dynamics of this molecule in the energy range probed by spectroscopic experiments in the infrared and microwave regions. The torsional transition frequencies calculated from this potential and the ab initio torsional inverse effective mass function are within 2 cm(-1) of the available experimental values. Furthermore, the computed contortional parameter rho of the rho-axis system Hamiltonian is also in excellent agreement with that obtained from spectral analyses of acetaldehyde.     

Combination transitions due to stretching and librations of OH⁻ ions in LiNbO₃

A new absorption band has been detected at 4009 cm?1 in stoichiometric LiNbO? single crystals. Based on present and earlier experiments and recent calculations, this band has been assigned as a combination transition involving the OH stretching and an OH librational mode. The librational mode participating in this combination is of lower fundamental frequency than that contributing to the combination band at 4415 cm1 observed by Gr?ne and Kapphan [J. Phys. Condens. Matter 7, 3051 (1995)].     

Perturbative treatment of the electron-correlation contribution to the diagonal Born-Oppenheimer correction

A perturbative scheme for the treatment of electron-correlation effects on the diagonal Born-Oppenheimer correction (DBOC) is suggested. Utilizing the usual Moller-Plesset partitioning of the Hamiltonian formulas for first and second orders (termed as MP1 and MP2) are obtained by expanding the wave function in the corresponding coupled-cluster expressions for the DBOC[J. Gauss et al., J. Chem. Phys. 125, 144111 (2006)]. The obtained expressions are recast in terms of one- and two-particle density matrices in order to take advantage of existing analytic second-derivative implementations for many-body methods. Test calculations show that both MP1 and MP2 recover large fractions (on average 90% and 95%, respectively) of the coupled-cluster singles and doubles (CCSD) electron-correlation corrections to the DBOC and thus render the suggested MP treatments cost-effective (though still accurate) alternatives to high-level coupled cluster (CC) treatments. The applicability of the MP1 and MP2 schemes for treating DBOC is demonstrated in calculations for the atomization energies of benzene, naphthalene, anthracene, and tetracene. The corresponding corrections are surprisingly large (about 0.6 kJmol for benzene, 1.1 kJmol for naphthalene, 1.5 kJmol for anthracene, and 1.8 kJmol for tetracene) with the electron-correlation corrections reducing the corresponding Hartree-Fock self-consistent field values by 25%-30%.     

Apparent clustering of intermediate-redshift galaxies as a probe of dark energy

We show that the apparent redshift-space clustering of galaxies in the redshift range of 0.2-0.4 provides surprisingly useful constraints on dark-energy components in the Universe, because of the right balance between the density of objects and the survey depth. We apply Fisher matrix analysis to the luminous red galaxies in the Sloan Digital Sky Survey, as a concrete example. Possible degeneracies in the evolution of the equation of state and the other cosmological parameters are clarified.     

On a phenomenon of Turán concerning the summands of partitions

Turán [12] proved that for almost all pairs of partitions of an integer, the proportion of common parts is very high, that is greater than \({\frac{1}{2} - \varepsilon}\) with \({\varepsilon > 0}\) arbitrarily small. In this paper we prove that this surprising phenomenon persists when we look only at the summands in a fixed arithmetic progression.