By David Sholl, Janice A Steckel
Demonstrates how an individual in math, technology, and engineering can grasp DFT calculations
Density useful conception (DFT) is among the most often used computational instruments for learning and predicting the houses of remoted molecules, bulk solids, and fabric interfaces, together with surfaces. even though the theoretical underpinnings of DFT are particularly advanced, this booklet demonstrates that the elemental innovations underlying the calculations are basic sufficient to be understood via somebody with a historical past in chemistry, physics, engineering, or arithmetic. The authors exhibit how the frequent availability of strong DFT codes permits scholars and researchers to use this crucial computational strategy to a vast variety of basic and utilized difficulties.
Density sensible thought: a pragmatic creation bargains a concise, easy-to-follow creation to the major innovations and useful purposes of DFT, targeting plane-wave DFT. The authors have decades of expertise introducing DFT to scholars from quite a few backgrounds. The ebook for that reason deals numerous positive aspects that experience confirmed to be important in permitting scholars to grasp the topic, together with:
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Extra info for Density functional theory: a practical introduction
This observation has a simple physical interpretation: the fcc crystal structure of Cu is more stable than the simple cubic crystal structure. This conclusion is not surprising since Cu is in reality an fcc metal, but it is pleasing to ﬁnd that our DFT calculations are in agreement with physical reality. We can also compare our calculated lattice constant with the experimental result. From the curve in Fig. 64 A ˚ and B0 140 GPa for Cu. 62 A GPa. For both quantities, our predictions are very close (although not equal to) the experimental values.
For every one of these choices, we are deﬁning just one atom in the supercell, and the repetition of the supercell in space creates the simple cubic structure. Putting the atom at (0,0,0) may seem like the best choice from an aesthetic point of view, although (a/2,a/2,a/2) is also appealing because it puts the atom in the middle of the supercell. The point to remember is that any of these choices is mathematically equivalent, so they are all equally good from the point of view of doing an actual calculation.
This inexactness exists because the exact functional that the Hohenberg –Kohn theorem applies to is not known. So any time you (or anyone else) performs a DFT calculation, there is an intrinsic uncertainty that exists between the energies calculated with DFT and the true ground-state energies of the Schro¨dinger equation. In many situations, there is no direct way to estimate the magnitude of this uncertainty apart from careful comparisons with experimental measurements. As you read further through this book, we hope you will come to appreciate that there are many physical situations where the accuracy of DFT calculations is good enough to make powerful predictions about the properties of complex materials.
Density functional theory: a practical introduction by David Sholl, Janice A Steckel