Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighboring P-donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position, and interdonor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, while the magnitude of the double occupancy probability can affect the error rate.

Spin-detection in a quantum electromechanical shuttle system

We study the electrical transport of a harmonically bound, single-molecule C-60 shuttle operating in the Coulomb blockade regime, i.e. single electron shuttling. In particular, we examine the dependance of the tunnel current on an ultra-small stationary force exerted on the shuttle. As an example, we consider the force exerted on an endohedral N@C-60 by the magnetic field gradient generated by a nearby nanomagnet. We derive a Hamiltonian for the full shuttle system which includes the metallic contacts, the spatially dependent tunnel couplings to the shuttle, the electronic and motional degrees of freedom of the shuttle itself and a coupling of the shuttle's motion to a phonon bath. We analyse the resulting quantum master equation and find that, due to the exponential dependence of the tunnel probability on the shuttle-contact separation, the current is highly sensitive to very small forces. In particular, we predict that the spin state of the endohedral electrons of N@C-60 in a large magnetic gradient field can be distinguished from the resulting current signals within a few tens of nanoseconds. This effect could prove useful for the detection of the endohedral spin-state of individual paramagnetic molecules such as N@C-60 and P@C-60, or the detection of very small static forces acting on a C-60 shuttle.

Ultramicroporous membranes for hydrogen separation

Fuel cell systems offer excellent efficiencies when compared to internal combustion engines, which result in reduced fuel consumption and greenhouse gas emissions. One of the areas requiring research for the success of fuel cell technology is the H2 fuel purification to reduce CO, which is a poison to fuel cells. Molecular sieve silica (MSS) membranes have a potential application in this area. In this work showed activated transport, a characteristic of ultramicroporous (dp

Thermal Cycling Stability of Silica Membranes for Gas Separation

Hydrogen is being seen as an alternative energy carrier to conventional hydrocarbons to reduce greenhouse gas emissions. High efficiency separation technologies to remove hydrogen from the greenhouse gas, carbon dioxide, are therefore in growing demand. Traditional thermodynamic separation systems utilise distillation, absorption and adsorption, but are limited in efficiency at compact scales. Molecular sieve silica (MSS) membranes can perform this separation as they have high permselectivity of hydrogen to carbon dioxide, but their stability under thermal cycling is not well reported. In this work we exposed a standard MSS membrane and a carbonised template MSS (CTMSS) membrane to thermal cycling from 100 to 450°C. The standard MSS and carbonised template CTMSS membranes both showed permselectivity of helium to nitrogen dropping from around 10 to 6 in the first set of cycles, remaining stable until the last test. The permselectivity drop was due to small micropore collapse, which occurred via structure movement during cycling. Simulating single stage membrane separation with a 50:50 molar feed of H2:CO2, H2 exiting the permeate stream would start at 79% and stabilise at 67%. Higher selectivity membranes showed less of a purity drop, indicating the margin at which to design a stable membrane separation unit for CO2 capture.

Molecular sieve silica membranes for H2/CO separation

Efficient separation of fuel gas (H2) from other gases in reformed gas mixtures is becoming increasingly important in the development of alternative energy systems. A highly efficient and new technology available for these separations is molecular sieve silica (MSS) membranes derived from tetraethyl-orthosilicate (TEOS). A permeation model is developed from an analogous electronic system and compared to transport theory to determine permeation, selectivity and apparent activation of energy based on experimental values. Experimental results for high quality membranes show single gas permselectivity peaking at 57 for H2/CO at 150°C with a H2 permeation of 5.14 x 10^-8 mol.m^-2.s^-1.Pa^-1. Higher permeance was also achieved, but at the expense of selectivity. This is the case for low quality membranes with peak H2 permeation at 1.78 x 10-7 mol.m-2.s-1.Pa-1 at 22°C and H2/CO permselectivity of 4.5. High quality membranes are characterised with positive apparent activation energy while the low quality membranes have negative values. The model had a good fit of r-squared of 0.99-1.00 using the experimental data.

Molecular Sieve Silica (MSS) Membranes for Gas Separation and Reaction Processes

Weakly branched silica films formed by the two-step sol-gel process allow for the formation of high selectivity membranes for gas separation. 29Si NMR and gas permeation showed that reduced crosslinking leads to He/CH4 selectivity improvement from 300 to 1000. Applied in membrane reactor for cyclohexane conversion to benzene, conversions were achieved at 14 fold higher than a conventional reactor at 250°C. Hydrothermal stability studies showed that carbon templating of silica is required for hydrothermally stable membranes. From our work it was shown that with correct application of chemistry, practical membrane systems can be built to suit gas separation (e. g. hydrogen fuel) and reactor systems.

Hydrothermal stable templated molecular sieve silica (TMSS) membranes for gas separation

In this work we compare the hydrothermal stability performance of a Templated Molecular Sieve Silica (TMSS) membrane against a standard, non-templated Molecular Sieve Silica (MSS) membrane. The tests were carried under dry and wet (steam) conditions for single gas (He, H2, CO and CO2) at 1-2 atm membrane pressure drop at 200oC. Single gas TMSS membrane H2, permeance and H2/CO permselectivity was found to be 2.05 x 10-8 mols.m-2.s-1.Pa-1 and 15, respectively. The MSS membrane showed similar selectivity, but increased overall flux. He permeance through membranes decayed at a rate of 4-5 x 10-10 mols.m-2.s-1.Pa-1 per day regardless of membrane ambience (dry or wet). Although H2/CO permselectivity of the TMSS membrane slightly improved from 15 to 18 after steam testing, the MSS membrane resulted in significant reduction from 16 to 8.3. In addition, membrane regeneration after more than 50 days resulted in the TMSS membrane reverting to its original permeation levels while no significant improvements were observed for the MSS membra ne. Results showed that the TMSS membrane had enhanced hydrothermal stability and regeneration ability.

Hydrothermal Stability of Modified Silica Membranes for Gas Separation

A new class of hybrid molecular sieve silica (MSS) membranes is developed and tested against standard and organic templated membranes. The hybrid membrane is synthesized by the standard sol-gel process, integrating a template (methyltriethoxysilane - MTES) and a C6 surfactant (triethylhexylammonium bromide) into the silica film matrix. After hydro treatment under a relative humidity of 96% for 50h, the hybrid membrane shows no changes in its gas separation capabilities or energy of mobility. The structural characteristics and integrity of the hybrid membrane are retained due to a high concentration of organophilic functional groups and alkoxides observed using 29 Si NMR. In contrast, the structural integrity of the membranes prepared with non-templated films deteriorated during the hydro treatment due to a large percentage of silanol groups (Si-OH) which react with water. The hybrid membranes underwent a decrease in the H2/CO2 selectivity of only 1% whereas for the non-templated membrane a 21% decrease was observed. The transport mechanism of the hybrid membranes is activated as permeation increased with temperature. The activation energy for the permeation of H2 is positive while negative for CO2. The H2 permeation obtained was 3x 10 -8 mol.m -2 .s -1 .Pa -1 and permselectivities for H2/CO2 and H2/N2 varied between 1-7 and 31-34, respectively.

Hydrostability and Scaling Up Molecular Sieve Silica (MSS) Membranes for H2/CO Separation in Fuel Cell Systems

MSS membranes are a good candidate for CO cleanup in fuel cell fuel processing systems due to their ability to selectively permeate H2 over CO via molecular sieving. Successfully scaled up tubular membranes were stable under dry conditions to 400°C with H2 permeance as high as 2 x 10-6 mol.m-2.s^-1.Pa^-1 at 200 degrees C and H2/CO selectivity up to 6.4, indicating molecular sieving was the dominant mechanism. A novel carbonised template molecular sieve silica (CTMSS) technology gave the scaled up membranes resilience in hydrothermal conditions up to 400 degrees C in 34% steam and synthetic reformate, which is required for use in fuel cell CO cleanup systems.

Entanglement between a qubit and the environment in the spin-boson model

The quantitative description of the quantum entanglement between a qubit and its environment is considered. Specifically, for the ground state of the spin-boson model, the entropy of entanglement of the spin is calculated as a function of α, the strength of the ohmic coupling to the environment, and ɛ, the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For ɛ=0, the entanglement increases monotonically with α, until it becomes maximal for α→1-. For fixed ɛ>0, the entanglement is a maximum as a function of α for a value, α=αM

Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.