Search results for " function"
showing 10 items of 9395 documents
Conformation of the galactose ring adopted in solution and in crystalline form as determined by experimental and DFT 1H NMR and single-crystal X-ray …
2003
The solution-state conformations of various galactose derivatives were determined by comparison of the experimental (1)H-(1)H vicinal coupling constants to those calculated using density functional theory (DFT) at the B3LYP/cc-pVTZ//B3LYP/6-31G(d,p) level of theory. The agreement between the experimental and calculated vicinal coupling constants for 1,2:3,4-di-O-isopropylidene-alpha-d-galactopyranose was good, thereby confirming an (O)S(2) skew conformation for it and its derivatives on the basis of their similar observed couplings. Single-crystal X-ray analysis of 1,2:3,4-di-O-isopropylidene-6-O-(3,4,6-tri-O-acetyl-2-deoxy-2-N-phthalimido-beta-d-glucopyranosyl)-alpha-d-galactopyranose and …
One-bond 1 J (15 N,H) coupling constants at sp2 -hybridized nitrogen of Schiff bases, enaminones and similar compounds: A theoretical study
2020
1 J(15 N,H) coupling constants for enaminones and NH-forms of intramolecularly hydrogen-bonded Schiff bases as model compounds for sp2 -hybridized nitrogen atoms are evaluated using density functional theory (DFT) to find the optimal functionals and basis sets. Ammonia is used as a test molecule and its one-bond coupling constant is compared with experiment. A methylamine Schiff base of a truncated molecule of gossypol is used for checking the performance of selected B3LYP, O3LYP, PBE, BHandH, and APFD density functionals and standard, modified, and dedicated basis sets for coupling constants. Both in vacuum and in chloroform, modeled by the simple continuum model of solvent, the modified b…
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
2000
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …
Propagation of uncertainties in the Skyrme energy-density-functional model
2013
Parameters of nuclear energy-density-functionals (EDFs) are always derived by an optimization to experimental data. For the minima of appropriately defined penalty functions, a statistical sensitivity analysis provides the uncertainties of the EDF parameters. To quantify theoretical errors of observables given by the model, we studied the propagation of uncertainties within the UNEDF0 Skyrme-EDF approach. We found that typically the standard errors rapidly increase towards neutron rich nuclei. This can be linked to large uncertainties of the isovector coupling constants of the currently used EDFs.
Spurious finite-size instabilities in nuclear energy density functionals
2013
It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functi…
Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations
1985
We are going to describe our work on the quantum and classical statistical mechanics of some exactly integrable non-linear one dimensional systems. The simplest is the non-linear Schrodinger equation (NLS) $$i{\psi _t} = - {\psi _{XX}} + 2c{\psi ^ + }\psi \psi $$ (1) where c, the coupling constant, is positive. The others are the sine- and sinh-Gordon equations (sG and shG) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi $$ (1.2) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sinh \phi $$ (1.3)
A statistical study of the additivity of substituent effects on the5J(HH) long-range coupling constant of the formyl proton in substituted benzaldehy…
1982
The additivity of chloro and hydroxy substituent effects on the formyl proton spin-spin coupling constants with the meta ring proton, 5J(HH), has been tested with 15 chlorinated benzaldehydes and hydroxybenzaldehydes by multiple linear regression analysis. No general additivity rule was detected with whole data. Using benzaldehyde as the reference substance, a good correlation was achieved for p-hydroxybenzaldehydes. The same reference compound was not suitable for o-hydroxy derivatives; a much better correlation was observed using o-hydroxybenzaldehyde as a reference compound in the latter case.
Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polariz…
2009
Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) in the Kohn-Sham (KS) complete basis set (CBS) limit. Correlation-consistent cc-pVxZ and cc-pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ-pVxZ, unc-ccJ-pVxZ, and aug-cc-pVTZ-J) and polarization-consistent pc-n and pcJ-n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT-predicted isotropic shieldings, spin-spin values, and the experimenta…
Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin-spin coupling constants (SSCC) using polari…
2009
Efficient B3LYP and BHandH density functionals were used to estimate methanol's nuclear magnetic isotropic shieldings and spin–spin coupling constants in the basis set limit. Polarization-consistent pcS-n and pcJ-n (n = 0, 1, 2, 3 and 4), and segmented contracted XZP, where X = D, T, Q and 5, basis sets were used and the results fitted with simple mathematical formulas. The performance of the methods was assessed from comparison with experiment and higher level calculations. 1J(CH) and 3J(HH) values were determined from very diluted solutions in deuterochloroform and compared with theoretical predictions. The agreement between complete basis set (CBS) density functional theory (DFT) predict…
Model predictive control for continuous lactide ring‐opening polymerization processes
2020
International audience; Polylactic acid (PLA) is an attractive environment-friendly thermoplastic that is bio-sourced and biodegradable. PLA is industrially produced by the ring-opening polymerization of Lactide. This reaction is sensitive to drifts in the operating conditions and impurities in the raw materials that may affect the reaction rate as well as the polymer properties, which can be very costly in continuous processes. It is therefore crucial to employ a control strategy that allows recovering the nominal conditions and maintaining the desired properties and conversion level in case of drift. Three control strategies are discussed in this paper: Proportional-Integral controller (P…