Stability conditions for the solutions of the Half-Projected Hartree-Fock scheme. The lithium-hydride ground state

4 págs.; 1 fig.; 2 tabs.The stability conditions for the solutions of a two-unrestricted-determinant function (the half-projected Hartree-Fock function) are deduced from the necessary requirements for the minimization of the energy functional. The theory is applied to the case of the LiH ground state, in order to investigate the various solutions encountered in the variational problem. It is found that the two lowest solutions are local minima. The number of these solutions is estimated and their significance discussed as a function of the nuclear separation. © 1977 The American Physical Society.Peer Reviewe

An analysis of the methyl rotation dynamics in the S0 (X̃ 1A1) and T1 (ã 3A2) states of thioacetone, (CH3)2 CS and (CD 3)2 CS from pyrolysis jet spectra

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetone (CH3)2CS/(CD3)2 CS have been recorded over the region 16 800-18 500 cm-1 using the pyrolysis jet spectroscopic technique. The responsible electronic transition, T 1 ←-S0, ã 3 A ″ ← X̃ 1A1, results from an n → π* electron promotion and gives rise to a pattern of vibronic bands that were attributed to activity of the methyl torsion and the sulphur out-of-plane wagging modes. The intensities of the torsional and wagging progressions in the excitation spectra were interpreted in terms of a C2υ-Cs molecular distortion of the triplet molecule from its singlet ground state equilibrium structure. A complete unrestricted Hartree-Fock (UHF) ab initio molecular orbital (MO) structural optimization of the T1 state predicted that the sulphur was displaced by 27.36° from the molecular plane and the methyl groups were rotated by 10.93° in clockwise-counterclockwise directions. Restricted Hartree-Fock (RHF) calculations were used to generate the F(θ1,θ2) potential surface governing methyl rotation for the S0 state. This was incorporated into a two-dimensional Hamiltonian, symmetrized for the G36 point group and solved variationally for the torsional frequencies. The calculated frequencies of 159.97/118.94 for the ν17 (b1) mode of S0 (CH3)2CS/(CD3)2 CS were found to agree with the experimental values, 153.2/114.7 cm-1. © 1991 American Institute of Physics.The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for financial support of this work. D. J. C. acknowledges the support of the National Science Foundation through Grant No. CHE-8914403.Peer Reviewe

CCSD(T) Study of CD3-O-CD3 and CH3-O-CD3 Far-Infrared Spectra

From a vibrationally corrected 3D potential energy surface determined with highly correlated ab initio calculations (CCSD(T)), the lowest vibrational energies of two dimethyl-ether isotopologues, 12CH3–16O–12CD3 (DME-d3) and 12CD3–16O–12CD3 (DME-d6), are computed variationally. The levels that can be populated at very low temperatures correspond to the COC-bending and the two methyl torsional modes. Molecular symmetry groups are used for the classification of levels and torsional splittings. DME-d6 belongs to the G36 group, as the most abundant isotopologue 12CH3–16O–12CH3 (DME-h6), while DME-d3 is a G18 species. Previous assignments of experimental Raman and far-infrared spectra are discussed from an effective Hamiltonian obtained after refining the ab initio parameters. Because a good agreement between calculated and experimental transition frequencies is reached, new assignments are proposed for various combination bands corresponding to the two deuterated isotopologues and for the 020 → 030 transition of DME-d6. Vibrationally corrected potential energy barriers, structural parameters, and anharmonic spectroscopic parameters are provided. For the 3N – 9 neglected vibrational modes, harmonic and anharmonic fundamental frequencies are obtained using second-order perturbation theory by means of CCSD and MP2 force fields. Fermi resonances between the COC-bending and the torsional modes modify DME-d3 intensities and the band positions of the torsional overtones

Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.Comment: 62 pages, no figures. Corrected error in computation of coupling coefficients, added new selection rule and an appendix on energy and angular momentum of mode

Asteroseismology and Interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within Astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.Comment: Version as published in The Astronomy and Astrophysics Review, Volume 14, Issue 3-4, pp. 217-36

Treatment Patterns and Use of Resources in Patients With Tuberous Sclerosis Complex: Insights From the TOSCA Registry

Tuberous Sclerosis Complex (TSC) is a rare autosomal-dominant disorder caused by mutations in the TSC1 or TSC2 genes. Patients with TSC may suffer from a wide range of clinical manifestations; however, the burden of TSC and its impact on healthcare resources needed for its management remain unknown. Besides, the use of resources might vary across countries depending on the country-specific clinical practice. The aim of this paper is to describe the use of TSC-related resources and treatment patterns within the TOSCA registry. A total of 2,214 patients with TSC from 31 countries were enrolled and had a follow-up of up to 5 years. A search was conducted to identify the variables containing both medical and non-medical resource use information within TOSCA. This search was performed both at the level of the core project as well as at the level of the research projects on epilepsy, subependymal giant cell astrocytoma (SEGA), lymphangioleiomyomatosis (LAM), and renal angiomyolipoma (rAML) taking into account the timepoints of the study, age groups, and countries. Data from the quality of life (QoL) research project were analyzed by type of visit and age at enrollment. Treatments varied greatly depending on the clinical manifestation, timepoint in the study, and age groups. GAB Aergics were the most prescribed drugs for epilepsy, and mTOR inhibitors are dramatically replacing surgery in patients with SEGA, despite current recommendations proposing both treatment options. mTOR inhibitors are also becoming common treatments in rAML and LAM patients. Forty-two out of the 143 patients (29.4%) who participated in the QoL research project reported inpatient stays over the last year. Data from non-medical resource use showed the critical impact of TSC on job status and capacity. Disability allowances were more common in children than adults (51.1% vs 38.2%). Psychological counseling, social services and social worker services were needed by <15% of the patients, regardless of age. The long-term nature, together with the variability in its clinical manifestations, makes TSC a complex and resource-demanding disease. The present study shows a comprehensive picture of the resource use implications of TSC

Newly Diagnosed and Growing Subependymal Giant Cell Astrocytoma in Adults With Tuberous Sclerosis Complex: Results From the International TOSCA Study

The onset and growth of subependymal giant cell astrocytoma (SEGA) in tuberous sclerosis complex (TSC) typically occurs in childhood. There is minimal information on SEGA evolution in adults with TSC. Of 2,211 patients enrolled in TOSCA, 220 of the 803 adults (27.4%) ever had a SEGA. Of 186 patients with SEGA still ongoing in adulthood, 153 (82.3%) remained asymptomatic, and 33 (17.7%) were reported to ever have developed symptoms related to SEGA growth. SEGA growth since the previous scan was reported in 39 of the 186 adults (21%) with ongoing SEGA. All but one patient with growing SEGA had mutations in TSC2. Fourteen adults (2.4%) were newly diagnosed with SEGA during follow-up, and majority had mutations in TSC2. Our findings suggest that surveillance for new or growing SEGA is warranted also in adulthood, particularly in patients with mutations in TSC2

A theoretical determination of the methyl and aldehydic torsion far-infrared spectrum of propanal-d0 with the vibrational zero point correction

7 pages, 1 figure, 8 tables.The methyl and aldehydic torsions far-infrared (FIR) spectrum of standard propanal is determined theoretically taking into account the vibrational zero point energy (ZPE) of the remaining small amplitude vibration modes in an anharmonic approach. For this purpose, the potential energy function obtained in a previous calculation at the 6-311(3df,p) restricted Hartree–Fock/second-order Møller–Plesset level [J. Chem. Phys. 109, 2279 (1998)] is modified for the anharmonic ZPE corrections. With this corrected potential for the ZPE, the kinetic parameters, as well as the electric dipole moment variations, the FIR frequencies, and intensities for the methyl and aldehyde torsions of propanal were determined theoretically using a two-dimensional approach. The calculated torsional band structures of propanal determined without and with the ZPE corrections were compared between themselves and with the available experimental data. It is found that the theoretical calculations permit one to reproduce and assign 24 of the 25 observed bands. In the same way, the introduction of the ZPE corrections is seen to yield more satisfactory frequency values for the aldehyde torsion, double quanta, and methyl–aldehyde combination bands.The authors acknowledge the financial assistance of the Mexican CONACYT through Grant No. 400200-5-2542E and to the CICYT of Spain for the economical support under Contract No. PQU2000-1164.Peer reviewe

Ab initio calculations and analysis of the torsional spectra of dimethylamine and dimethylphosphine

In the present paper, ab initio calculations at MP2/RHF level are performed with different basis sets 6-31G(d,p), 6-311G(d,p), and 6-311(df,p) to determine the potential energy functions, the kinetic parameters, and the dipole moment components as a function of the double methyl rotation in dimethylamine (DMA) and dimethylphosphine (DMP). From the potential energy and kinetic parameters, the torsional energy levels and torsional functions are determined, and from the dipole moment variations, the far infrared spectra are synthesized by calculating both the frequencies and the intensities. The results are in relatively good agreement with experimental spectra. Calculations confirm the assignments performed with the experimental potentials fitted with only five terms. The calculations, however, allow to reassign the observed band at 239.8 cm-1 in DMA and at 177.2 cm-1 in DMP to the superimposition of two different transitions: the 03→04 third sequence and an 10→11 vibrationally excited fundamental. © 1996 American Institute of Physics.This work has been supported by the European Union under the Human Capital and Mobility Scheme (contract CHRZ CT 93-0157). The authors also acknowledge the fi- nancial assistance from the ‘‘Comision Interministerial de Ciencias y Technologia’’ of Spain through grant no. PB 93- 0185.Peer Reviewe

Ab initio determination of band structures of vibrational spectra of non-rigid molecules. Applications to methylamine and dimethylamine

The ab initio determination of the band structures of infrared spectra is described giving as examples the methyl torsion and amine wagging in methylamine and the double torsion in dimethylamine. In addition, the influence of the amine hydrogen symmetric bending and the CNC skeleton symmetric bending is considered in methylamine and dimethylamine, respectively. For this purpose, the potential energy sufaces and kinetic parameters are determined at the RHF/MP2 levels with large basis sets. The numerical results are fitted as a function of the vibrational angles to conveniently symmetry adapted functional forms. The Schrödinger equations for the nuclear motions solved by expanding the solutions into products of trigonometric functions. From the energy levels, the vibrational functions and the electric dipole moment variations the bands locations and intensities are determined. The calculated spectra are compared with the available experimental data. In the case of methylamine, the torsional splittings and frequencies are relatively well reproduced, whereas the wagging frequencies appear to be slightly too high. In the case, of dimethylamine, the symmetric and antisymmmetric torsion modes are very well reproduced, whereas the CNC bending frequencies appear also to be too high. © 1999 Academic Press Inc.Y.G.S. and M.L.S. wish to thank the >Comisión lnterministerial de Ciencias y Tecnología> of Spain for financial support through grant nQ PB93-0185, M.V. would like to thank the CSIC (Spain) and CONACYT (Mexico) for a sabbatical fellowship.Peer Reviewe