Permutation blocking path integral Monte Carlo simulations of degenerate electrons at finite temperature

We analyse the simulation of strongly degenerate electrons at finite temperature using the recently introduced permutation blocking path integral Monte Carlo (PB‐PIMC) method [T. Dornheim et al., New J. Phys. 17 , 073017 (2015)]. As a representative example, we consider electrons in a harmonic confinement and carry out simulations for up to P = 2000 so‐called imaginary‐time propagators – an important convergence parameter within the PIMC formalism. This allows us to study the P‐dependence of different observables of the configuration space in the Monte Carlo simulations and of the fermion sign problem. We find a surprisingly persisting effect of the permutation blocking for large P, which is explained by comparing different length scales. Finally, we touch upon the uniform electron gas in the warm dense matter regime.     

Coherent State Path Integral for the Harmonic Oscillator and a Spin Particle in a Constant Magnetic field

Definition and formulas for harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism and its relation with the partition function of a system are also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level and then used to find its continuum limit using various regularizations. The computation of the path integral for a particle of spin s put in a constant magnetic field is carried out using harmonic oscillator coherent states and spin coherent states, with a careful analysis of infinitesimal terms (in 1/N where N is the number of time slices) appearing in the Lagrangian. A mapping of the spin system into a CP¹ model is shown explicitly. The theory of a spinless particle in the field of a magnetic monopole and its relation with the spin system are explained. The equivalence of these two models is established up to infinitesimal order by the introduction of an external field correction. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral.     

Path integral approach for Stark broadening of Lyman lines in hydrogen plasma

New results for Lyman lines from hydrogen plasmas are presented using the path integral approach. The influence of plasma components (electrons and ions) on the radiator is analysed separately. The ionic contribution is treated within the path integral approach, while the electronic contribution is estimated by the standard collision operator. The Stark effect, including the ion quadrupole contribution, is considered. The time‐dependent ionic microfield is treated within the path integral approximation using the model microfield method (MMM). The comparison with the quantum statistical approach is performed using a wide range of temperatures (T = 10⁴–10⁷ K) and electron densities (N_e = 10²³–10²⁶ m^?3). Good agreement is mainly obtained for low density and high temperature.     

Correlation Functions for MN/SN Orbifolds

We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M ^N /S _N , where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is “universal” in the sense that it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions. The condition for the genus zero contribution to the 3-point functions to be non-vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of N – this is a manifestation of the stringy exclusion principle. Received: 20 July 2000 / Accepted: 17 December 2000     

Nucleophilic reactivity of thiolate, hydroxide and phenolate ions towards a model O-arylated diazeniumdiolate prodrug in aqueous and cationic surfactant media

The kinetics of aromatic nucleophilic substitution of the nitric oxide‐generating diazeniumdiolate ion, DEA/NO, by thiols (L ‐glutathione, L ‐cysteine, DL ‐homocysteine, 1‐propanethiol, 2‐mercaptoethanol, and sodium thioglycolate) from the prodrug, DNP‐DEA/NO, has been examined in aqueous solution and in solutions of cationic DOTAP vesicles. Second‐order rate constants in buffered aqueous solutions (k_RS‐ = 3.48–30.9 M^?1 s^?1; 30 °C) gave a linear Brønsted plot (β_nuc = 0.414 ± 0.068) consistent with the rate‐limiting S_NAr nucleophilic attack by thiolate ions. Cationic DOTAP vesicles catalyze the thiolysis reactions with rate enhancements between 11 and 486‐fold in Tris‐HCl buffered solutions at pH 7.4. The maximum rate increase was obtained with thioglycolate ion. Thiolysis data are compared to data for nucleophilic displacement by phenolate (k_PhO‐ = 0.114 M^?1 s^?1) and hydroxide (k_OH‐ = 1.82 × 10^?2 M^?1 s^?1, 37 °C) ions. The base hydrolysis reaction is accelerated by CTAB micelles and DODAC vesicles, with the vesicles being ca 3‐fold more effective as catalysts. Analysis of the data using pseudo‐phase ion‐exchange (PIE) formalism implies that the rate enhancement of the thiolysis and base hydrolysis reactions is primarily due to reactant concentration in the surfactant pseudo‐phase. Copyright © 2009 John Wiley & Sons, Ltd.     

Ground state and excited state properties of ethylene isomers studied by a combined Feynman path integral-ab initio approach

Ground state and excited state properties of ethylene, C₂H₄, and several ethylene isomers have been studied by Feynman path integral Monte Carlo (PIMC) simulations. The PIMC treatment of the atomic nuclei has been combined with different electronic Hamiltonians in order to analyse the influence of the nuclear degrees of freedom on electronic quantities. Electronic expectation values at the minimum of the potential energy surface (PES) have been compared with PIMC based ensemble averaged values. Ensemble averaged quantities have been derived by Hamiltonians of the ab initio type and a tight-binding (TB) one-electron model. The combined influence of anharmonicities in the interatomic potential and the quantum fluctuations of the atomic nuclei lead to ensemble averaged bondlengths r _g which are significantly larger than the parameters r _e, at the minimum of the PES. The implications of this bond length elongation for the electronic properties of ethylene are discussed. The occupied canonical molecular orbitals (CMOs) of ethylene are destabilized under the influence of the nuclear degrees of freedom while virtual CMOs are stabilized. These shifts of one-electron energies suggest a comparison of electronic excitation energies at the minimum of the PES with PIMC based ensemble averages. The quantum fluctuations of the nuclei cause a strong redistribution in the intensities of electronic transitions. Transitions, which are dipole allowed in the planar D_2h geometry of ethylene, lose intensity under the influence of nuclear quantum effects, and vice versa for electronic excitations that are dipole forbidden under D_2h symmetry. This ‘vibrational borrowing’ is enhanced with decreasing atomic masses. The Feynman centroid density has been used to calculate the anharmonic vibrational wavenumbers of C₂H₄ and C₂D₄. The results of the present PIMC simulations have been employed to emphasize general problems of electronic structure calculations based on a single nuclear configuration (i.e. the configuration at the minimum of the PES).     

Electroluminescence enhancement in ultraviolet organic light‐emitting diode with graded hole‐injection and ‐transporting structure

Electroluminescent intensity and external quantum efficiency (EQE) in ultraviolet organic light‐emitting diodes (UV OLEDs) have been remarkably enhanced by using a graded hole‐injection and ‐transporting (HIT) structure of MoO₃/N,N ′‐bis(naphthalen‐1‐yl)‐N,N ′‐bis(phenyl)‐benzidine/MoO₃/4,4′‐bis(carbazol‐9‐yl)biphenyl (CBP). The graded‐HIT based UV OLED shows superior short‐wavelength emis‐ sion with spectral peak of ～410 nm, maximum electroluminescent intensity of 2.2 mW/cm² at 215 mA/cm² and an EQE of 0.72% at 5.5 mA/cm². Impedance spectroscopy is employed to clarify the enhanced hole‐injection and ‐transporting capacity of the graded‐HIT structure. Our results provide a simple and effective approach for constructing efficient UV OLEDs. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Electronic effects of heterocyclic ring systems as evaluated with the aid of 13C and 15N NMR chemical shifts and NBO analysis

The electronic effects of the 5‐ and 6‐membered heterocyclic rings on the C?N? N unit of five different hydrazone derivatives of pyridine‐2‐, ‐3‐ and ‐4‐carbaldehydes, pyrrole‐2‐carbaldehyde, furan‐2‐ and ‐3‐carbaldehydes and thiophene‐2‐ and ‐3‐carbaldehydes have been studied with the aid of ¹³C and ¹⁵N NMR measurements together with the natural bond orbital (NBO) analysis. As model compounds are used the corresponding substituted benzaldehyde derivatives. The polarization of the C?N unit of the hydrazone functionality of the heteroaryl derivatives occurs in an analogous manner with that of phenyl derivatives. The electron‐withdrawing heteroaryl groups destabilize and the electron‐donating groups stabilize the positive charge development at the C?N carbon while the effect on the negative charge development is opposite. The ¹⁵N NMR chemical shift of the C?N and C?N? N nitrogens and the NBO charges at C?N? N unit can be correlated with the replacement substituent constants σ of the heteroaryl groups. ¹³C NMR shifts of the C?N carbon of N,N‐dialkylhydrazones of the heteroarenecarbaldehydes can be correlated with a dual parameter equation possessing the polar substituent constant σ* of the heteroaryl group and the electronegativity of the heteroatom as variables. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesis and X‐ray structures of unexpected 2‐O‐(5‐deoxy‐1,2‐O‐isopropylidene‐α‐D‐glucofuranos‐5‐yloxy)quinoxalines

Reaction of 3‐methyl‐2(1H)‐quinoxalinone ( 4) and 2(1H)‐quinoxalinone ( 5) with 5,6‐anhydro‐1,2‐O‐isopropylidene‐ α‐D ‐glucofuranose 6 gives the unexpected O‐glucoquinoxalines derivatives by the intermediary novel intramolecular rearrangement of 5,6‐anhydro‐1,2‐O‐isopropylidene‐α‐D ‐glucofuranose to the corresponding 3,6‐anhydro form. The obtained O‐glucoquinoxalines 7,8 were identified by NMR spectroscopy. The X‐ray crystal structures have been determined at room temperature. Moreover, a solid–solid phase transition has been detected at 198.9 K for O‐glucoquinoxalines 7 and the structure of the low‐temperature phase has been solved at 188 K. Copyright © 2009 John Wiley & Sons, Ltd.     

Vibrational spectroscopy and crystal structure analysis of two polymorphs of the di‐amino acid peptide cyclo(L‐Glu‐L‐Glu)

Cyclo(L ‐Glu‐L ‐Glu) has been crystallised in two different polymorphic forms. Both polymorphs are monoclinic, but form 1 is in space group P2₁ and form 2 is in space group C2. Raman scattering and FT‐IR spectroscopic studies have been conducted for the N,O‐protonated and deuterated derivatives. Raman spectra of orientated single crystals, solid‐state and aqueous solution samples have also been recorded. The different hydrogen‐bonding patterns for the two polymorphs have the greatest effect on vibrational modes with N H and CO stretching character. DFT (B3‐LYP/cc‐pVDZ) calculations of the isolated cyclo(L ‐Glu‐L ‐Glu) molecule predict that the minimum energy structure, assuming C₂ symmetry, has a boat conformation for the diketopiperazine ring with the two L ‐Glu side chains being folded above the ring. The calculated geometry is in good agreement with the X‐ray crystallographic structures for both polymorphs. Normal coordinate analysis has facilitated the band assignments for the experimental vibrational spectra. Copyright © 2009 John Wiley & Sons, Ltd.     

Breakdown conditions and thermal instability in air

Summary Reduced electric fields (E/N) responsible for electrical breakdown in air have been calculated by solving a stationary Boltzmann equation including superelastic vibrational collisions. The results show a decrease ofE/N with increasing gas temperature. The possibility of air instability due to chemical processes producing electrons is then investigated by calculating the threshold of this instability as a function of a characteristic time for heat dissipation τ.     

Vibrational spectroscopic studies of the structure of di‐amino acid peptides. Part II: cyclo(L‐Asp‐L‐Asp) in the solid state and in aqueous solution

Solid‐state protonated and N,O‐deuterated Fourier transform infrared (IR) and Raman scattering spectra together with the protonated and deuterated Raman spectra in aqueous solution of the cyclic di‐amino acid peptide cyclo(L ‐Asp‐L ‐Asp) are reported. Vibrational band assignments have been made on the basis of comparisons with previously cited literature values for diketopiperazine (DKP) derivatives and normal coordinate analyses for both the protonated and deuterated species based upon DFT calculations at the B3‐LYP/cc‐pVDZ level of the isolated molecule in the gas phase. The calculated minimum energy structure for cyclo(L ‐Asp‐L ‐Asp), assuming C₂ symmetry, predicts a boat conformation for the DKP ring with both the two L ‐aspartyl side chains being folded slightly above the ring. The CO stretching vibrations have been assigned for the side‐chain carboxylic acid group (e.g. at 1693 and 1670 cm⁻¹ in the Raman spectrum) and the cis amide I bands (e.g. at 1660 cm⁻¹ in the Raman spectrum). The presence of two bands for the carboxylic acid CO stretching modes in the solid‐state Raman spectrum can be accounted for by factor group splitting of the two nonequivalent molecules in a crystallographic unit cell. The cis amide II band is observed at 1489 cm⁻¹ in the solid‐state Raman spectrum, which is in agreement with results for cyclic di‐amino acid peptide molecules examined previously in the solid state, where the DKP ring adopts a boat conformation. Additionally, it also appears that as the molecular mass of the substituent on the C^α atom is increased, the amide II band wavenumber decreases to below 1500 cm⁻¹; this may be a consequence of increased strain on the DKP ring. The cis amide II Raman band is characterized by its relatively small deuterium shift (29 cm⁻¹), which indicates that this band has a smaller N H bending contribution than the trans amide II vibrational band observed for linear peptides. Copyright © 2009 John Wiley & Sons, Ltd.     

Vibrational spectra and crystal structure of the di‐amino acid peptide cyclo(L‐Met‐L‐Met): comparison of experimental data and DFT calculations

Experimental Raman and FT‐IR spectra of solid‐state non‐deuterated and N‐deuterated samples of cyclo(L ‐Met‐L ‐Met) are reported and discussed. The Raman and FT‐IR results show characteristic amide I vibrations (Raman: 1649 cm⁻¹, infrared: 1675 cm⁻¹) for molecules exhibiting a cis amide conformation. A Raman band, assigned to the cis amide II vibrational mode, is observed at ∼1493 cm⁻¹ but no IR band is observed in this region. Cyclo(L ‐Met‐L ‐Met) crystallises in the triclinic space group P1 with one molecule per unit cell. The overall shape of the diketopiperazine (DKP) ring displays a (slightly distorted) boat conformation. The crystal packing employs two strong hydrogen bonds, which traverse the entire crystal via translational repeats. B3‐LYP/cc‐pVDZ calculations of the structure of the molecule predict a boat conformation for the DKP ring, in agreement with the experimentally determined X‐ray structure. Copyright © 2009 John Wiley & Sons, Ltd.     

Modeling of supersonic plasma flow in the scrape-off layer

The substantial drop of the plasma temperature along magnetic field lines with increasing plasma density is one of the main features in tokamak divertors. As a result the temperature gradient at the divertor plates becomes very steep and the boundary condition normally applied for the parallel Mach number M at the target, M_t = 1, cannot be satisfied. In this case the value of M_t based on the general form of the Bohm criterion, M_t  1, has to be determined from the continuity of plasma parameters.In the present paper a new approach to resolve the Mach number at the target for such a situation is proposed. This method avoids the singularity problem that arises by treating the particle balance and parallel motion equations in a differential form. Instead, the integral representation of the equations is formulated for an arbitrary form of particle and momentum sources. The approach can also take into account transport perpendicular to the magnetic field lines.The proposed method is demonstrated on the example of a one-dimensional stationary model for the scrape-off layer (SOL) plasma and includes the continuity-, parallel momentum- and heat transfer equations. The recycled neutrals are described in the diffusion approximation. In the case of low density the normal condition M_t = 1 is satisfied and the results are in agreement with the two-point model. At high enough plasma density solutions with the supersonic flow at the divertor plates, M_t > 1, are found. These states correspond to a partially detached plasma with a temperature of a few eV.     

Conformational analysis of 3,3‐dimethyl‐3‐silathiane, 2,3,3‐trimethyl‐3‐silathiane and 2‐trimethylsilyl‐3,3‐dimethyl‐3‐silathiane—preferred conformers,barriers to ring inversion and substituent effects

The first conformational analysis of 3‐silathiane and its C‐substituted derivatives, namely, 3,3‐dimethyl‐3‐silathiane 1 , 2,3,3‐trimethyl‐3‐silathiane 2 , and 2‐trimethylsilyl‐3,3‐dimethyl‐3‐silathiane 3 was performed by using dynamic NMR spectroscopy and B3LYP/6‐311G(d,p) quantum chemical calculations. From coalescence temperatures, ring inversion barriers ΔG^≠ for 1 and 2 were estimated to be 6.3 and 6.8 kcal/mol, respectively. These values are considerably lower than that of thiacyclohexane (9.4 kcal/mol) but slightly higher than the one of 1,1‐dimethylsilacyclohexane (5.5 kcal/mol). The conformational free energy for the methyl group in 2 (?ΔG° = 0.35 kcal/mol) derived from low‐temperature ¹³C NMR data is fairly consistent with the calculated value. For compound 2 , theoretical calculations give ΔE value close to zero for the equilibrium between the 2 ‐Me_ax and 2 ‐Me_eq conformers. The calculated equatorial preference of the trimethylsilyl group in 3 is much more pronounced (?ΔG° = 1.8 kcal/mol) and the predominance of the 3 ‐SiMe_{3 eq} conformer at room temperature was confirmed by the simulated ¹H NMR and 2D NOESY spectra. The effect of the 2‐substituent on the structural parameters of 2 and 3 is discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Quantum system in contact with a thermal environment: Rigorous treatment of a simple model

We study the quantum dynamics of a particle of massM in an external potentialV(Q), interacting with a simple model environment—a harmonic chain of 2N particles with massm and spring constantk. The classical version of this model was studied by Rubin and is equivalent to standard models of a particle interacting with a phonon bath. Settingm=m*/L andk=k*L, we prove that for a suitable class of potentialsV and initial states ₀, the time evolution of the massM particle converges, whenN andL , to the time evolution governed by the Quantum Langevin Equation (QLE) which has been found by Ford, Kac and Mazur. Furthermore we show that, for this class of potentials, the QLE has a unique solution for all positive times, such solution can be expressed as a convergent expansion in the deviation ofV(Q) from a harmonic potential. The equilibrium properties of the particle with massM can be expressed in terms of an integral, over path space, with a Gaussian measure which has mean zero and covariance proportional to ; where is the friction constant, andh is the Plancks' constant (divided by 2).Supported in part by AFOSR Grant No. 86-0010     

Electron spin resonance and quantum critical phenomena in VOx multiwall nanotubes

Basing on the high frequency (60 GHz) electron spin resonance study of the VO_x multiwall nanotubes (VO_x ‐NTs) carried out in the temperature range 4.2–200 K we report: (i) the first direct experimental evidence of the presence of the antiferromagnetic dimers in VO_x ‐NTs and (ii) the observation of an anomalous low temperature growth of the magnetic susceptibility for quasi‐free spins, which obey the power law χ (T)～1/T ^α with the exponent α ≈ 0.6 in a wide temperature range 4.2–50 K. We argue that the observed departures from the Curie–Weiss behaviour manifest the onset of the quantum critical regime and formation of the Griffiths phase as a magnetic ground state of these spin species. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-Point Functions for MN/SN Orbifolds¶with?= 4 Supersymmetry

The D1–D5 system is believed to have an “orbifold point” in its moduli space where its low energy theory is a ?=4 supersymmetric sigma model with target space M ^N /S _N , where M is T ⁴ or K3. We study correlation functions of chiral operators in CFTs arising from such a theory. We construct a basic class of chiral operators from twist fields of the symmetric group and the generators of the superconformal algebra. We find explicitly the 3-point functions for these chiral fields at large N; these expressions are “universal” in that they are independent of the choice of M. We observe that the result is a significantly simpler expression than the corresponding expression for the bosonic theory based on the same orbifold target space. Received: 29 March 2001 / Accepted: 20 January 2002     

High‐accuracy X‐ray absorption spectra from mM solutions of nickel (II) complexes with multiple solutions using transmission XAS

A new approach is introduced for determining X‐ray absorption spectroscopy (XAS) spectra on absolute and relative scales using multiple solutions with different concentrations by the characterization and correction of experimental systematics. This hybrid technique is a development of standard X‐ray absorption fine structure (XAFS) along the lines of the high‐accuracy X‐ray extended range technique (XERT) but with applicability to solutions, dilute systems and cold cell environments. This methodology has been applied to determining absolute XAS of bis(N‐n‐propyl‐salicylaldiminato) nickel(II) and bis(N‐i‐propyl‐salicylaldiminato) nickel(II) complexes with square planar and tetrahedral structures in 15 mM and 1.5 mM dilute solutions. It is demonstrated that transmission XAS from dilute systems can provide excellent X‐ray absorption near‐edge structure (XANES) and XAFS spectra, and that transmission measurements can provide accurate measurement of subtle differences including coordination geometries. For the first time, (transmission) XAS of the isomers have been determined from low‐concentration solutions on an absolute scale with a 1–5% accuracy, and with relative precision of 0.1% to 0.2% in the active XANES and XAFS regions after inclusion of systematic corrections.