Hybrid functional calculations of the Al impurity in silica: Hole localization and electron paramagnetic resonance parameters

We performed first-principle calculations based on the supercell and cluster approaches to investigate the neutral Al impurity in smoky quartz. Electron paramagnetic resonance measurements suggest that the oxygens around the Al center undergo a polaronic distortion which localizes the hole being on one of the four oxygen atoms. We find that the screened exchange hybrid functional successfully describes this localization and improves on standard local density approaches or on hybrid functionals that do not include enough exact exchange such as B3LYP. We find a defect level at about 2.5 eV above the valence band maximum, corresponding to a localized hole in a O 2p orbital. The calculated values of the g tensor and the hyperfine splittings are in excellent agreement with experiment.Comment: 5 pages, 2 figures, 1 tabl

Theory of Orbital Magnetization in Solids

In this review article, we survey the relatively new theory of orbital magnetization in solids-often referred to as the "modern theory of orbital magnetization"-and its applications. Surprisingly, while the calculation of the orbital magnetization in finite systems such as atoms and molecules is straight forward, in extended systems or solids it has long eluded calculations owing to the fact that the position operator is ill-defined in such a context. Approaches that overcome this problem were first developed in 2005 and in the first part of this review we present the main ideas reaching from a Wannier function approach to semi-classical and finite-temperature formalisms. In the second part, we describe practical aspects of calculating the orbital magnetization, such as taking k-space derivatives, a formalism for pseudopotentials, a single k-point derivation, a Wannier interpolation scheme, and DFT specific aspects. We then show results of recent calculations on Fe, Co, and Ni. In the last part of this review, we focus on direct applications of the orbital magnetization. In particular, we will review how properties such as the nuclear magnetic resonance shielding tensor and the electron paramagnetic resonance g-tensor can elegantly be calculated in terms of a derivative of the orbital magnetization

Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry

We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently developed hierarchical tensor representations, in particular tensor trains which are matrix product states in physics language. The discrete equations of full CI approximation applied to the electronic Schr\"odinger equation is casted into a tensorial framework in form of the second quantization. A further approximation is performed afterwards by tensor approximation within a hierarchical format or equivalently a tree tensor network. We establish the (differential) geometry of low rank hierarchical tensors and apply the Driac Frenkel principle to reduce the original high-dimensional problem to low dimensions. The DMRG algorithm is established as an optimization method in this format with alternating directional search. We briefly introduce the CC method and refer to our theoretical results. We compare this approach in the present discrete formulation with the CC method and its underlying exponential parametrization.Comment: 15 pages, 3 figure

The structure of the Au(111)/methylthiolate interface : new insights from near-edge X-ray absorption spectroscopy and X-ray standing waves

The local structure of the Au(111)([square root of]3×[square root of]3)R30°-methylthiolate surface phase has been investigated by S K-edge near-edge s-ray absorption fine structure (NEXAFS) both experimentally and theoretically and by experimental normal-incidence x-ray standing waves (NIXSW) at both the C and S atomic sites. NEXAFS shows not only excitation into the intramolecular sigma* S–C resonance but also into a sigma* S–Au orbital perpendicular to the surface, clearly identifying the local S headgroup site as atop a Au atom. Simulations show that it is not possible, however, to distinguish between the two possible adatom reconstruction models; a single thiolate species atop a hollow-site Au adatom or a dithiolate moiety comprising two thiolate species bonded to a bridge-bonded Au adatom. Within this dithiolate moiety a second sigma* S–Au orbital that lies near parallel to the surface has a higher energy that overlaps that of the sigma* S–C resonance. The new NIXSW data show the S–C bond to be tilted by 61° relative to the surface normal, with a preferred azimuthal orientation in , corresponding to the intermolecular nearest-neighbor directions. This azimuthal orientation is consistent with the thiolate being atop a hollow-site Au adatom, but not consistent with the originally proposed Au-adatom-dithiolate moiety. However, internal conformational changes within this species could, perhaps, render this model also consistent with the experimental data

Dual kinetic balance approach to basis set expansions for the Dirac equation

A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated for finite basis sets constructed from B splines by calculating the one-loop self-energy correction for a hydrogenlike ion.Comment: 14 pages, 1 tabl

The mystery of relationship of mechanics and field in the many-body quantum world

We have revealed three fatal errors incurred from a blind transferring of quantum field methods into the quantum mechanics. This had tragic consequences because it produced crippled model Hamiltonians, unfortunately considered sufficient for a description of solids including superconductors. From there, of course, Fr\"ohlich derived wrong effective Hamiltonian, from which incorrect BCS theory arose. 1) Mechanical and field patterns cannot be mixed. Instead of field methods applied to the mechanical Born-Oppenheimer approximation we have entirely to avoid it and construct an independent and standalone field pattern. This leads to a new form of the Bohr's complementarity on the level of composite systems. 2) We have correctly to deal with the center of gravity, which is under the field pattern "materialized" in the form of new quasipartiles - rotons and translons. This leads to a new type of relativity of internal and external degrees of freedom and one-particle way of bypassing degeneracies (gap formation). 3) The possible symmetry cannot be apriori loaded but has to be aposteriori obtained as a solution of field equations, formulated in a general form without translational or any other symmetry. This leads to an utterly revised view of symmetry breaking in non-adiabatic systems, namely Jahn-Teller effect and superconductivity. These two phenomena are synonyms and share a unique symmetry breaking.Comment: 24 pages, 9 sections; remake of abstract, introduction and conclusion; more physics, less philosoph

Relativistic J-matrix method

The relativistic version of the J-matrix method for a scattering problem on the potential vanishing faster than the Coulomb one is formulated. As in the non-relativistic case it leads to a finite algebraic eigenvalue problem. The derived expression for the tangent of phase shift is simply related to the non-relativistic case formula and gives the latter as a limit case. It is due to the fact that the used basis set satisfies the ``kinetic balance condition''.Comment: 21 pages, RevTeX, accepted for publication in Phys. Rev.

Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies

A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes for some cases of two electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^4S(p^3)$ state using appropriate coordinate maps and wavefunction symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into 3D space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wavefunctions.Comment: 7 pages, 7 figure

An extension of the coupled-cluster method: A variational formalism

A general quantum many-body theory in configuration space is developed by extending the traditional coupled cluter method (CCM) to a variational formalism. Two independent sets of distribution functions are introduced to evaluate the Hamiltonian expectation. An algebraic technique for calculating these distribution functions via two self-consistent sets of equations is given. By comparing with the traditional CCM and with Arponen's extension, it is shown that the former is equivalent to a linear approximation to one set of distribution functions and the later is equivalent to a random-phase approximation to it. In additional to these two approximations, other higher-order approximation schemes within the new formalism are also discussed. As a demonstration, we apply this technique to a quantum antiferromagnetic spin model.Comment: 15 pages. Submitted to Phys. Rev.

Centre-of-mass separation in quantum mechanics: Implications for the many-body treatment in quantum chemistry and solid state physics

We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all non-adiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.Comment: 39 pages, 11 sections, 3 appendice