311 research outputs found
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
Non-isotropic cusp conditions and regularity of the electron density of molecules at the nuclei
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-Ď benzene-water interaction via the dangling OH stretch of water with the delocalised Ď 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
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