Lunar landing and long-range earth re-entry guidance by application of perturbation theory

1964 ◽  
Vol 1 (2) ◽  
pp. 191-196 ◽  
Author(s):  
HENRY C. LESSING ◽  
PHILLIPS J. TUNNELL ◽  
ROBERT E. COATE
Keyword(s):  
Perturbation Theory ◽  
Long Range ◽  
Lunar Landing ◽  
Entry Guidance

scholarly journals Simplified Tuning of Long-Range Corrected Density Functionals for Use in Symmetry-Adapted Perturbation Theory

2021 ◽  
Author(s):  
Montgomery Gray ◽  
John Herbert
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Behavior ◽  
Long Range ◽  
System Size ◽  
Second Order ◽  
Density Functionals ◽  
Hole Making ◽  
Large Systems ◽  
Automated Tuning ◽  
Order Dispersion

Long considered a failure, second-order symmetry-adapted perturbation theory (SAPT) based on Kohn-Sham orbitals, or SAPT(KS), can been resurrected for semiquantitative purposes using long-range corrected (LRC) density functionals whose asymptotic behavior is adjusted separately for each monomer. As in other contexts, correct asymptotic behavior can be enforced via "optimal tuning" of LRC functionals, based on the ionization energy theorem, but the tuning procedure is tedious, expensive for large systems, and comes with a troubling dependence on system size. Here, we show that essentially identical results are obtained using an automated tuning procedure based on the size of the exchange hole, making tuned "SAPT(wKS)" fast and convenient. In conjunction with SAPT-based methods that sidestep second-order dispersion, this procedure achieves benchmark-quality interaction energies, along with the usual SAPT energy decomposition, without the hassle of system-specific tuning.

Long-range potentials and dipole moments of the CO electronic states converging to the ground dissociation limit

2020 ◽  
Vol 22 (21) ◽  
pp. 12058-12067
Author(s):  
Vladimir G. Ushakov ◽  
Vladimir V. Meshkov ◽  
Aleksander Yu. Ermilov ◽  
Andrey V. Stolyarov ◽  
Iouli E. Gordon ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Dipole Moment ◽  
Potential Energy ◽  
Long Range ◽  
First Principles ◽  
Dipole Moments ◽  
Electronic States ◽  
Dissociation Limit ◽  
Moment Functions ◽  
Range Perturbation

The potential-energy and dipole-moment functions for six electronic states are obtained both analytically, in the framework of long-range perturbation theory, and numerically, by using first-principles methods.

scholarly journals Perturbation theory for very long-range potentials

2013 ◽  
Vol 185 ◽  
pp. 20-25 ◽  
Author(s):  
L. Escamilla ◽  
J. Torres-Arenas ◽  
A.L. Benavides
Keyword(s):  
Perturbation Theory ◽  
Long Range
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