scholarly journals Pure and Hybrid SCAN, rSCAN, and r2SCAN: Which One Is Preferred in KS- and HF-DFT Calculations, and How Does D4 Dispersion Correction Affect This Ranking?

Molecules ◽  
2021 ◽  
Vol 27 (1) ◽  
pp. 141
Author(s):  
Golokesh Santra ◽  
Jan M. L. Martin
Keyword(s):  
Dft Calculations ◽  
The Self ◽  
The Other ◽  
Dispersion Correction ◽  
Exchange Correlation ◽  
Self Consistent

Using the large and chemically diverse GMTKN55 dataset, we have tested the performance of pure and hybrid KS-DFT and HF-DFT functionals constructed from three variants of the SCAN meta-GGA exchange-correlation functional: original SCAN, rSCAN, and r2SCAN. Without any dispersion correction involved, HF-SCANn outperforms the two other HF-DFT functionals. In contrast, among the self-consistent variants, SCANn and r2SCANn offer essentially the same performance at lower percentages of HF-exchange, while at higher percentages, SCANn marginally outperforms r2SCANn and rSCANn. However, with D4 dispersion correction included, all three HF-DFT-D4 variants perform similarly, and among the self-consistent counterparts, r2SCANn-D4 outperforms the other two variants across the board. In view of the much milder grid dependence of r2SCAN vs. SCAN, r2SCAN is to be preferred across the board, also in HF-DFT and hybrid KS-DFT contexts.

scholarly journals Implicit algorithms for eigenvector nonlinearities

2021 ◽  
Author(s):  
Elias Jarlebring ◽  
Parikshit Upadhyaya
Keyword(s):  
Eigenvalue Problems ◽  
The Self ◽  
The Other ◽  
Convergence Theory ◽  
System Matrix ◽  
Established Method ◽  
Nonlinear Eigenvalue Problems ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

AbstractWe study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit viewpoint. More precisely, we change the Newton update equation in a way that the next iterate does not only appear linearly in the update equation. Although the modifications of the update equation make the methods implicit, we show how corresponding iterates can be computed explicitly. Therefore, we can carry out steps of the implicit method using explicit procedures. In several cases, these procedures involve a solution of standard eigenvalue problems. We propose two modifications, one of the modifications leads directly to a well-established method (the self-consistent field iteration) whereas the other method is to our knowledge new and has several attractive properties. Convergence theory is provided along with several simulations which illustrate the properties of the algorithms.

scholarly journals A quantum mechanical investigation of the cohesive forces of metallic copper

1935 ◽  
Vol 151 (874) ◽  
pp. 585-602 ◽  
Keyword(s):  
Lattice Constant ◽  
Noble Metals ◽  
Metallic Copper ◽  
Direct Interaction ◽  
The Self ◽  
The Other ◽  
Consistent Field ◽  
Valence Electrons ◽  
Self Consistent ◽  
Self Consistent Field

The calculations of Wigner and Seitz have shown that the Bloch theory is capable of yielding, at any rate roughly, the lattice energy, lattice constant, and compressibility of the metal sodium, and it seems probable that their method could be applied with equal success to the other alkalis. On the other hand, no calculations have as yet been made for the noble metals. Such a calculations is given in this paper. The noble metals differ from the alkalis in having cores which are much larger compared with the atomic volume than those of the alkalis, and the main purpose of this paper is to see whether direct interaction between the pressibility, etc. We have also attempted to find out why the noble metals have the face-centred cubic structure, while the alkalis are body-centred. In 2 we calculate the wave functions and energies of the valence electrons (4 s ) of metallic copper. We chose copper for this calculation, because a self-consistent field due to Hartree is available. Wigner and Seitz did not use the self-consistent field for sodium, but a half empirical potential function for the sodium ion, calculated by Prokofjew from the observed term values. This potential therefore includes implicitly the exchange interaction between the valence electrons and the inner shells, so far as this may be represented by an electrostatic potential. With the self-consistent field the exchange has to be taken into account explicitly; we have done this by solving approximately, instead of the simple Schroedinger equation, Fock’s wave equation, which includes the exchange. Apart from this the calculation in 2 is entirely analogous to that of Wigner and Seitz. It will be shown that for copper this calculations given at least the right order of magnitude for the lattice constant and for the heat of vaporization, but a totally incorrect value for the compressibility.

Monte Carlo Simulation of Diffusion with Uniform Sinks and Sources for Vacancies

2005 ◽  
Vol 237-240 ◽  
pp. 1168-1173 ◽  
Author(s):  
Jaroslav Ženíšek ◽  
Jiří Svoboda ◽  
Franz Dieter Fischer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Model ◽  
Kirkendall Effect ◽  
The Self ◽  
The Other ◽  
Other Hand ◽  
Self Consistent

A new concept of generation and annihilation of vacancies at uniform sinks and sources for vacancies is incorporated into the standard Monte Carlo model for vacancy mediated diffusion. This model enables to treat the vacancy wind as well as the deformation of the specimen and the shift of the Kirkendall plane. The Monte Carlo model is used for the testing of the recent phenomenological theories of diffusion by Darken, Manning and Moleko. The agreement with the self-consistent Moleko theory is excellent. On the other hand the agreement with the classical Darken theory used very often for the explanation of the Kirkendall effect is rather poor.

scholarly journals Self-consistent field, with exchange, for Cl -

1936 ◽  
Vol 156 (887) ◽  
pp. 45-62 ◽  
Keyword(s):  
Excited States ◽  
The Self ◽  
The Other ◽  
Negative Ion ◽  
Field Problem ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Difference

Quantitative solutions by Fock's equations for the self-consistent field, including exchange effects, have now been obtained for the normal state of Na + , and for the normal and some excited states of neutral Li and Na, by Fock and Petrashen, and for the normal and the (2 s ) (2 p ) 3 P and 1 P excited states of neutral Be, by the present authors. The work here described was undertaken as the first step in carrying out the solution of Fock's equations for heavier atoms; calculations for Cu + , in progress at the time of writing, will carry this a step further. The effect of the inclusion of exchange terms on the self-consistent field may be expected to be particularly large for a negative ion, on account of the sensiticeness of the wave function of the outer ( nl ) group of such an ion (and, to a less extent, of those of the other groups of the outer shell also). This, of course, is likely to make the process of solution of Fock's equations more than usually difficult and lengthy for a negative ion, and made the project of obtaining such a solution appear somewhat ambitions; but, on the other calculations, are greatest when the difference from the solution of the self-consistent field problem without exchange is greatest, and for this reason it seemed desirable to carry out the solution of Fock's equations for at least one negative ion.

scholarly journals Noble Gases Encaged by the C60 Increase Their Chemical Reactivity

2017 ◽  
Vol 56 (3) ◽  
Author(s):  
Avelino Cortés-Santiago ◽  
Rubicelia Vargas ◽  
Jorge Garza
Keyword(s):  
Noble Gases ◽  
Chemical Reactivity ◽  
The Self ◽  
The Other ◽  
Inert Gases ◽  
Attractive Potential ◽  
Exchange Correlation ◽  
Exchange Correlation Potential ◽  
Interesting Conclusion ◽  
Correlation Potential

In this work, we use a spherical shell with an attractive potential to simulate the C<sub>60</sub> and its effects on, He, Ne, Ar and Kr when each atom is in the center of the sphere. Within the Kohn-Sham model, two exchange-correlation functionals were used; the main difference between these two functionals is that one incorporates explicitly the self-interaction correction and the correct asymptotic behavior of the exchange-correlation potential, and the other one does not contain such corrections. We found that the considered atoms are softer inside of the cage than when they are free. By using several chemical reactivity predictors as the electrodonating and electroaccepting powers, defined by Professor Gázquez <em>et al</em>. (<em>J. Phys. Chem. A</em> 2007, <em>111</em>, 1966), it is proved that the noble gases increase their chemical reactivity when they are immersed in the C<sub>60</sub>. Naturally, this conjecture must be confirmed by more realistic models, but at first glance this is a very interesting conclusion and opens a new possibility to obtain reactions with encaged inert gases.

Providing Freshmen with a Good “Starting-Block”

2019 ◽  
Vol 78 (1-2) ◽  
pp. 69-75 ◽  
Author(s):  
Mikaël De Clercq ◽  
Charlotte Michel ◽  
Sophie Remy ◽  
Benoît Galand
Keyword(s):  
The Self ◽  
The Other ◽  
Student Adjustment ◽  
Social Psychological ◽  
Pivotal Phase ◽  
Study Program ◽  
Study Task ◽  
The Social ◽  
Social Belonging ◽  
Intention To Persist

Abstract. Grounded in social-psychological literature, this experimental study assessed the effects of two so-called “wise” interventions implemented in a student study program. The interventions took place during the very first week at university, a presumed pivotal phase of transition. A group of 375 freshmen in psychology were randomly assigned to three conditions: control, social belonging, and self-affirmation. Following the intervention, students in the social-belonging condition expressed less social apprehension, a higher social integration, and a stronger intention to persist one month later than the other participants. They also relied more on peers as a source of support when confronted with a study task. Students in the self-affirmation condition felt more self-affirmed at the end of the intervention but didn’t benefit from other lasting effects. The results suggest that some well-timed and well-targeted “wise” interventions could provide lasting positive consequences for student adjustment. The respective merits of social-belonging and self-affirmation interventions are also discussed.

Stories and the Self

2020 ◽  
Vol 32 (2) ◽  
pp. 47-58 ◽  
Author(s):  
Stefan Krause ◽  
Markus Appel
Keyword(s):  
Meta Analysis ◽  
The Self ◽  
The Other ◽  
Lower Degree ◽  
Contrast Effects ◽  
Self Perception ◽  
Self Perceptions ◽  
Other Hand ◽  
The One ◽  
Implicit And Explicit

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.

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