Convergence of an s-wave calculation of the He ground state

The Configuration Interaction (CI) method using a large Laguerre basis restricted to l = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that the energy converges as Delta E^N approx A/N^(7/2) + B/N^(8/2) + >... where N is the number of Laguerre basis functions. The electron-electron delta-function expectation converges as Delta delta^N approx A/N^(5/2) + B/N^(6/2) + ... and the variational limit for the l = 0 basis is estimated as 0.1557637174(2) a_0^3. It was seen that extrapolation of the energy to the variational limit is dependent upon the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a non-optimal exponent if one wishes to extrapolate to the variational limit. An investigation of the Natural Orbital asymptotics revealed the energy converged as Delta E^N approx A/N^6 + B/N^7 + ... while the electron-electron delta-function expectation converged as Delta delta^N approx A/N^4 + B/N^5 + >... . The asymptotics of expectation values other than the energy showed fluctuations that depended on whether $N$ was even or odd.Comment: 12 pages, 10 figures, revtex format, submitted to Int.J.Quantum Chemistr

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

Convergence of the partial wave expansion of the He ground state

The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each l ranging from 0 to 12 resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron delta-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite in angular momentum using expansions of the type Delta X_J = A_X/(J+1/2)^p + B_X/(J+1/2)^(p+1) + ..., gave an energy accurate to 10^(-7) Hartree and a value of accurate to about 0.5%. Improved estimates of and , accurate to 10^(-8) Hartree and 0.01% respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J -> infty limit. Round-off errors were the main impediment to achieving even higher precision since determination of the radial and angular limits required the manipulation of very small energy and differences.Comment: 11 pages, 7 figures, revtex format, submitted to Int.J.Quantum Chemistr

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

Improvement of the noradrenergic symptom cluster following treatment with milnacipran

Depression has a major impact on social functioning. Decreased concentration, mental and physical slowing, loss of energy, lassitude, tiredness, and reduced self-care are all symptoms related to reduced noradrenergic activity. Depressed mood; loss of interest or pleasure; sleep disturbances; and feelings of worthlessness, pessimism, and anxiety are related to reduced activity of both serotonergic and noradrenergic neurotransmission. The importance of noradrenergic neurotransmission in social functioning is supported by studies with the specific norepinephrine reuptake inhibitor reboxetine. In healthy volunteers, reboxetine increases cooperative social behavior and social drive. A placebo-controlled study in depressed patients comparing reboxetine with the selective serotonin reuptake inhibitor (SSRI) fluoxetine showed significantly greater improvement in social adaptation with reboxetine. Two recent studies have examined the effect of the serotonin and norepinephrine reuptake inhibitor milnacipran on social adaptation. A study in depressed patients found that at the end of 8 weeks of treatment with milnacipran, 42.2% patients were in remission on the Social Adaptation Self-evaluation Scale (SASS). Another study in depressed workers or homemakers found that mean depression scores were significantly reduced after 2 weeks, whereas the SASS scores were significantly improved after 4 weeks. A preliminary study comparing depressed patients treated with milnacipran or the SSRI paroxetine showed that milnacipran treatment resulted in a greater number of patients in social remission. The available data thus suggest that milnacipran may improve social functioning, with a possibly greater effect than the SSRI paroxetine. These preliminary data suggest further evaluation of social dysfunction and its treatment outcome in future trials of milnacipran

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

Recurrence relations for four-electron integrals over Gaussian basis functions

In the spirit of the Head-Gordon-Pople algorithm, we report vertical, transfer and horizontal recurrence relations for the efficient and accurate computation of four-electron integrals over Gaussian basis functions. Our recursive approach is a generalization of our algorithm for three-electron integrals [J.~Chem.~Theory Comput.~12, 1735 (2016)]. The RRs derived in the present study can be applied to a general class of multiplicative four-electron operators. In particular, we consider various types of four-electron integrals that may arise in explicitly-correlated F12 methods.Comment: 11 pages, 3 figures and 2 table

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

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 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