Second‐Order Dispersion‐Energy Series for Axially Symmetric Molecules

1969 ◽  
Vol 10 (3) ◽  
pp. 539-544 ◽  
Author(s):  
Johannes H. van der Merwe ◽  
Alwyn J. van der Merwe
Keyword(s):  
Second Order ◽  
Axially Symmetric ◽  
Dispersion Energy ◽  
Order Dispersion

Second-Order Dispersion Energy Based on Multireference Description of Monomers

2018 ◽  
Vol 15 (2) ◽  
pp. 1016-1027 ◽  
Author(s):  
Michał Hapka ◽  
Michał Przybytek ◽  
Katarzyna Pernal
Keyword(s):  
Second Order ◽  
Dispersion Energy ◽  
Order Dispersion

scholarly journals Second-Order Exchange-Dispersion Energy Based on a Multireference Description of Monomers

2019 ◽  
Vol 15 (12) ◽  
pp. 6712-6723 ◽  
Author(s):  
Michał Hapka ◽  
Michał Przybytek ◽  
Katarzyna Pernal
Keyword(s):  
Second Order ◽  
Dispersion Energy

SECOND ORDER NUCLEAR QUADRUPOLE EFFECTS IN SINGLE CRYSTALS: PART I. THEORETICAL

1953 ◽  
Vol 31 (5) ◽  
pp. 820-836 ◽  
Author(s):  
G. M. Volkoff
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Single Crystals ◽  
Electric Quadrupole ◽  
Second Order ◽  
Order Effects ◽  
Axially Symmetric ◽  
Crystalline Electric Field ◽  
Resonance Frequencies ◽  
Principal Axes

The dependence of electric quadrupole splitting of nuclear magnetic resonance absorption lines in single crystals on crystal orientation in an external magnetic field is investigated theoretically following earlier work of Pound, of Volkoff, Petch, and Smellie, and of Bersohn. Explicit formulae are given, applicable to non axially symmetric crystalline electric field gradients (η ≠ 0), and valid up to terms of the second order in the quadrupole coupling constant [Formula: see text], for the dependence of the absorption frequencies on the angle of rotation of the crystal about any arbitrary axis perpendicular to the magnetic field. Some formulae including third order effects in Cz are also given. It is shown that an experimental study of the dependence of this splitting on the angles of rotation about any two arbitrary mutually perpendicular axes is sufficient, when second order effects are measurable, to yield the values of | Cz |, η, and the orientation of the principal axes of the electric field gradient tensor at the nuclear sites. In the case that the direction of one of the principal axes is known from crystal symmetry, a single rotation about this axis gives the complete information.A new method of determining nuclear spin I is proposed which depends on comparing first and second order shifts of the resonance frequencies of the strong inner line components. The method will be of interest in those cases where the total number 2I of line components can not be unambiguously ascertained owing to the outer line components being excessively broadened and weakened by crystal imperfections.

Large Signal Analysis of FM-AM Conversion in Dispersive Optical Fibers for PCM Systems Including Second Order Dispersion

2002 ◽  
Vol 21 (3) ◽  
pp. 193-203 ◽  
Author(s):  
R. S. Kaler ◽  
T. S. Kamal ◽  
Ajay K. Sharma ◽  
Sandeep K. Arya ◽  
R. A. Agarwala
Keyword(s):  
Optical Fibers ◽  
Signal Analysis ◽  
Second Order ◽  
Large Signal ◽  
Order Dispersion

Second-order dispersion interactions in π-conjugated polymers

2011 ◽  
Vol 134 (23) ◽  
pp. 234101 ◽  
Author(s):  
William Barford ◽  
Nattapong Paiboonvorachat ◽  
David Yaron
Keyword(s):  
Conjugated Polymers ◽  
Second Order ◽  
Dispersion Interactions ◽  
Order Dispersion

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.

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