Basis set expansion for inverse problems in plasma diagnostic analysis

2013 ◽  
Vol 84 (7) ◽  
pp. 073510 ◽  
Author(s):  
B. Jones ◽  
C. L. Ruiz
Keyword(s):  
Inverse Problems ◽  
Basis Set ◽  
Diagnostic Analysis ◽  
Plasma Diagnostic ◽  
Basis Set Expansion

Performance of Electronic Structure Methods for the Description of Hückel-Möbius Interconversions in Extended π-Systems

2019 ◽  
Author(s):  
Tatiana Woller ◽  
Ambar Banerjee ◽  
Nitai Sylvetsky ◽  
Xavier Deraet ◽  
Frank De Proft ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Basis Set ◽  
Dft Methods ◽  
Molecular Switching ◽  
Wide Range ◽  
Electronic Structure Methods ◽  
Explicitly Correlated ◽  
Relative Errors ◽  
The Stability ◽  
Basis Set Expansion

<p>Expanded porphyrins provide a versatile route to molecular switching devices due to their ability to shift between several π-conjugation topologies encoding distinct properties. Taking into account its size and huge conformational flexibility, DFT remains the workhorse for modeling such extended macrocycles. Nevertheless, the stability of Hückel and Möbius conformers depends on a complex interplay of different factors, such as hydrogen bonding, p···p stacking, steric effects, ring strain and electron delocalization. As a consequence, the selection of an exchange-correlation functional for describing the energy profile of topological switches is very difficult. For these reasons, we have examined the performance of a variety of wavefunction methods and density functionals for describing the thermochemistry and kinetics of topology interconversions across a wide range of macrocycles. Especially for hexa- and heptaphyrins, the Möbius structures have a pronouncedly stronger degree of static correlation than the Hückel and figure-eight structures, and as a result the relative energies of singly-twisted structures are a challenging test for electronic structure methods. Comparison of limited orbital space full CI calculations with CCSD(T) calculations within the same active spaces shows that post-CCSD(T) correlation contributions to relative energies are very minor. At the same time, relative energies are weakly sensitive to further basis set expansion, as proven by the minor energy differences between MP2/cc-pVDZ and explicitly correlated MP2-F12/cc-pVDZ-F12 calculations. Hence, our CCSD(T) reference values are reasonably well-converged in both 1-particle and n-particle spaces. While conventional MP2 and MP3 yield very poor results, SCS-MP2 and particularly SOS-MP2 and SCS-MP3 agree to better than 1 kcal mol<sup>-1</sup> with the CCSD(T) relative energies. Regarding DFT methods, only M06-2X provides relative errors close to chemical accuracy with a RMSD of 1.2 kcal mol<sup>-1</sup>. While the original DSD-PBEP86 double hybrid performs fairly poorly for these extended p-systems, the errors drop down to 2 kcal mol<sup>-1</sup> for the revised revDSD-PBEP86-NL, again showing that same-spin MP2-like correlation has a detrimental impact on performance like the SOS-MP2 results. </p>

Basis-Set Expansions of Relativistic Electronic Wave Functions

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Relativistic Quantum ◽  
Finite Basis ◽  
Wave Functions ◽  
Basis Set ◽  
Electronic Wave ◽  
Nonrelativistic Case ◽  
Hartree Fock ◽  
Electronic Wave Functions ◽  
Basis Set Expansion ◽  
Molecular Calculations

There have been several successful applications of the Dirac–Hartree–Fock (DHF) equations to the calculation of numerical electronic wave functions for diatomic molecules (Laaksonen and Grant 1984a, 1984b, Sundholm 1988, 1994, Kullie et al. 1999). However, the use of numerical techniques in relativistic molecular calculations encounters the same difficulties as in the nonrelativistic case, and to proceed to general applications beyond simple diatomic and linear molecules it is necessary to resort to an analytic approximation using a basis set expansion of the wave function. The techniques for such calculations may to a large extent be based on the methods developed for nonrelativistic calculations, but it turns out that the transfer of these methods to the relativistic case requires special considerations. These considerations, as well as the development of the finite basis versions of both the Dirac and DHF equations, form the subject of the present chapter. In particular, in the early days of relativistic quantum chemistry, attempts to solve the DHF equations in a basis set expansion sometimes led to unexpected results. One of the problems was that some calculations did not tend to the correct nonrelativistic limit. Subsequent investigations revealed that this was caused by inconsistencies in the choice of basis set for the small-component space, and some basic principles of basisset selection for relativistic calculations were established. The variational stability of the DHF equations in a finite basis has also been a subject of debate. As we show in this chapter, it is possible to establish lower variational bounds, thus ensuring that the iterative solution of the DHF equations does not collapse. There are two basically different strategies that may be followed when developing a finite basis formulation for relativistic molecular calculations. One possibility is to expand the large and small components of the 4-spinor in a basis of 2-spinors. The alternative is to expand each of the scalar components of the 4-spinor in a scalar basis. Both approaches have their advantages and disadvantages, though the latter approach is obviously the easier one for adapting nonrelativistic methods, which work in real scalar arithmetic.

Finite-basis-set expansion methods for scattering problems

1988 ◽  
Vol 38 (7) ◽  
pp. 3365-3371 ◽  
Author(s):  
Károly Ladányi ◽  
Péter Lévay ◽  
Barnabás Apagyi
Keyword(s):  
Finite Basis ◽  
Basis Set ◽  
Scattering Problems ◽  
Basis Set Expansion

scholarly journals Plasma diagnostics for planetary nebulae and H ii regions using N ii and O ii optical recombination lines

2011 ◽  
Vol 7 (S283) ◽  
pp. 432-433
Author(s):  
Ian A. McNabb ◽  
Xuan Fang ◽  
Xiao–Wei Liu ◽  
Peter J. Storey
Keyword(s):  
Plasma Diagnostics ◽  
Planetary Nebulae ◽  
Coupling Scheme ◽  
H Ii Regions ◽  
Diagnostic Analysis ◽  
Plasma Diagnostic ◽  
Intermediate Coupling ◽  
Physical Conditions ◽  
Cold Metal ◽  
Intermediate Coupling Scheme

AbstractWe carry out plasma diagnostic analysis for a number of planetary nebulae (PNe) and H ii regions. We use N ii and O ii optical recombination lines (ORLs) with new effective recombination coefficients calculated under the intermediate coupling scheme, for a range of electron temperatures (Te) and densities (Ne), and fitted against the most reliable measurements. Comparing Te derived from ORLs, collisionally excited lines (CELs), the hydrogen Balmer Jump, and/or He i if available, we find the relation Te (ORLs) < Te (He i) < Te (H i BJ) < Te (CELs), confirming the physical conditions in the bi-abundance model postulated by Liu et al., i.e. the nebula contains another cold, metal-rich and probably H-deficient component.

Genetic algorithms in plasma diagnostic analysis

2000 ◽  
Vol 42 (3) ◽  
pp. 337-346 ◽  
Author(s):  
A P Millar ◽  
D C McDonald ◽  
D A Diver
Keyword(s):  
Genetic Algorithms ◽  
Diagnostic Analysis ◽  
Plasma Diagnostic

Improving numerical integration through basis set expansion

2004 ◽  
Vol 112 (5-6) ◽  
pp. 410-418 ◽  
Author(s):  
Dew A. McCormack ◽  
Evert Jan Baerends ◽  
Erik van Lenthe ◽  
Nicholas C. Handy
Keyword(s):  
Numerical Integration ◽  
Basis Set ◽  
Basis Set Expansion

An “optimal” spawning algorithm for adaptive basis set expansion in nonadiabatic dynamics

2009 ◽  
Vol 130 (13) ◽  
pp. 134113 ◽  
Author(s):  
Sandy Yang ◽  
Joshua D. Coe ◽  
Benjamin Kaduk ◽  
Todd J. Martínez
Keyword(s):  
Basis Set ◽  
Nonadiabatic Dynamics ◽  
Basis Set Expansion
Sign in / Sign up

Export Citation Format

Share Document