Dealing with the exponential wall in electronic structure calculations

An alternative to Density Functional Theory are wavefunction based electronic structure calculations for solids. In order to perform them the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an {\it impurity} or {\it fragment} embedded in a {\it bath} which is treated at a much lower level than the former. This is the case in Density Matrix Embedding Theory (DMET) or Density Embedding Theory (DET). The latter are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a $H_{10}$ ring these differences are analyzed with the help of the method of increments.Comment: 19 pages, 5 figure

No slices on the space of generalized connections

On a fiber bundle without structure group the action of the gauge group (the group of all fiber respecting diffeomorphisms) on the space of (generalized) connections is shown not to admit slices.Comment: AmSTeX, diag.tex, 7 page

On the mixed Cauchy problem with data on singular conics

We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators whose principal part $Q_{2p}(D)$ essentially is the (complex) Laplace operator to a power, $\Delta^p$. We pose inital data on a singular conic divisor given by P=0, where $P$ is a homogeneous polynomial of degree $2p$. We show that this problem is uniquely solvable if the polynomial $P$ is elliptic, in a certain sense, with respect to the principal part $Q_{2p}(D)$

Ab-Initio Calculation of the Metal-Insulator Transition in Lithium rings

We study how the Mott metal-insulator transition (MIT) is affected when we have to deal with electrons with different angular momentum quantum numbers. For that purpose we apply ab-initio quantum-chemical methods to lithium rings in order to investigate the analogue of a MIT. By changing the interatomic distance we analyse the character of the many-body wavefunction and discuss the importance of the $s-p$ orbital quasi-degeneracy within the metallic regime. The charge gap (ionization potential minus electron affinity) shows a minimum and the static electric dipole polarizability has a pronounced maximum at a lattice constant where the character of the wavefunction changes from significant $p$ to essentially $s$-type. In addition, we examine rings with bond alternation in order to answer the question under which conditions a Peierls distortion occurs.Comment: 9 pages, 11 figure

Obtaining Wannier Functions of a Crystalline Insulator within a Hartree-Fock approach: Applications to LiF and LiCl

An ab initio Hartree-Fock approach aimed at directly obtaining the localized orthogonal orbitals (Wannier functions) of a crystalline insulator is described in detail. The method is used to perform all-electron calculations on the ground states of crystalline lithium fluoride and lithium chloride, without the use of any pseudo or model potentials. Quantities such as total energy, x-ray structure factors and Compton profiles obtained using the localized Hartree-Fock orbitals are shown to be in excellent agreement with the corresponding quantities calculated using the conventional Bloch-orbital based Hartree-Fock approach. Localization characteristics of these orbitals are also discussed in detail.Comment: 39 Pages, RevTex, 4 postscript figures, to appear in PRB15, January 9

Wavefunction-based correlated ab initio calculations on crystalline solids

We present a wavefunction-based approach to correlated ab initio calculations on crystalline insulators of infinite extent. It uses the representation of the occupied and the unoccupied (virtual) single-particle states of the infinite solid in terms of Wannier functions. Electron correlation effects are evaluated by considering virtual excitations from a small region in and around the reference cell, keeping the electrons of the rest of the infinite crystal frozen at the Hartree-Fock level. The method is applied to study the ground state properties of the LiH crystal, and is shown to yield rapidly convergent results.Comment: 6 pages, RevTex, to appear in Phys. Rev.