Positivity and lower bounds to the decay of the atomic one-electron density

We investigate properties of the spherically averaged atomic one-electron density rho~(r). For a rho~ which stems from a physical ground state we prove that rho~ > 0. We also give exponentially decreasing lower bounds to rho~ in the case when the eigenvalue is below the corresponding essential spectrum.Comment: 20 page

Non-isotropic cusp conditions and regularity of the electron density of molecules at the nuclei

We investigate regularity properties of molecular one-electron densities rho near the nuclei. In particular we derive a representation rho(x)=mu(x)*(e^F(x)) with an explicit function F, only depending on the nuclear charges and the positions of the nuclei, such that mu belongs to C^{1,1}(R^3), i.e., mu has locally essentially bounded second derivatives. An example constructed using Hydrogenic eigenfunctions shows that this regularity result is sharp. For atomic eigenfunctions which are either even or odd with respect to inversion in the origin, we prove that mu is even C^{2,\alpha}(R^3) for all alpha in (0,1). Placing one nucleus at the origin we study rho in polar coordinates x=r*omega and investigate rho'(r,omega) and rho''(r,omega) for fixed omega as r tends to zero. We prove non-isotropic cusp conditions of first and second order, which generalize Kato's classical result.Comment: 19 page

Analytic structure of many-body Coulombic wave functions

We investigate the analytic structure of solutions of non-relativistic Schr"odinger equations describing Coulombic many-particle systems. We prove the following: Let psi(x) with x=(x_1,...,x_N) in R^{3N} denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coalescence point, for which x_1=0 and the other electron coordinates do not coincide, and differ from 0, psi can be represented locally as psi(x) = psi^(1)(x) + |x_1|psi^(2)(x) with psi^(1), psi^(2) real analytic. A similar representation holds near two-electron coalescence points. The Kustaanheimo-Stiefel transform and analytic hypoellipticity play an essential role in the proof.Comment: 23 page

Probing the interaction between solid benzene and water using vacuum ultraviolet and infrared spectroscopy

We present results of a combined vacuum ultravioloet (VUV) and infrared (IR) photoabsorption study of amorphous benzene:water mixtures and layers to investigate the benzene-water interaction in the solid phase. UV spectra of 1:1, 1:10 and 1:100 benzene:water mixtures at 24 K reveal a concentration dependent shift in the energies of the 1B2u, 1B1u and 1E1u electronic states of benzene. All the electronic bands blueshift from pure amorphous benzene towards gas phase energies with increasing water concentration. IR results reveal a strong dOH-π benzene-water interaction via the dangling OH stretch of water with the delocalised π system of the benzene molecule. Although this interaction influences the electronic states of benzene with the benzenewater interaction causing a redshift in the electronic states from that of the free benzene molecule, the benzene-benzene interaction has a more significant effect on the electronic states of benzene. VUV spectra of benzene and water layers show evidence of non-wetting between benzene and water, characterised by Rayleigh scattering tails at wavelengths greater than 220 nm. Our results also show evidence of benzene-water interaction at the benzene-water interface affecting both the benzene and the water electronic states. Annealing the mixtures and layers of benzene and water show that benzene remains trapped within in/under water ice until water desorption near 160 K. These first systematic studies of binary amorphous mixtures in the VUV, supported with complementary IR studies, provide a deeper insight into the influence of intermolecular interactions on intramolecular electronic states with significant implications for our understanding of photochemical processes in more realistic astrochemical environments

The electron density is smooth away from the nuclei

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.Comment: 16 page

Ionic strength and calcium regulate membrane interactions of myelin basic protein and the cytoplasmic domain of myelin protein zero

The formation of a mature myelin sheath in the vertebrate nervous system requires specific protein-membrane interactions. Several myelin-specific proteins are involved in stacking lipid membranes into multilayered structures around axons, and misregulation of these processes may contribute to chronic demyelinating diseases. Two key proteins in myelin membrane binding and stacking are the myelin basic protein (MBP) and protein zero (P0). Other factors, including Ca2+, are important for the regulation of myelination. We studied the effects of ionic strength and Ca2+ on the membrane interactions of MBP and the cytoplasmic domain of P0 (P0ct). MBP and P0ct bound and aggregated negatively charged lipid vesicles, while simultaneously folding, and both ionic strength and calcium had systematic effects on these interactions. When decreasing membrane net negative charge, the level and kinetics of vesicle aggregation were affected by both salt and Ca2+. The effects on lipid membrane surfaces by ions can directly affect myelin protein-membrane interactions, in addition to signalling effects in myelinating glia.publishedVersio

Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to the rank--M multiconfiguration equations for a molecule with L fixed nuclei at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k}, phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.Comment: 15 page