Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

2019 ◽  
Vol 40 (29) ◽  
pp. 2563-2570 ◽  
Author(s):  
Martin Becker ◽  
Marek Sierka
Keyword(s):  
Density Functional Theory ◽  
Stress Tensor ◽  
Density Functional ◽  
Fast Multipole Method ◽  
Periodic Systems ◽  
Fast Multipole ◽  
Functional Theory ◽  
Density Fitting ◽  
Multipole Method

An improved scheme for the calculation of NMR chemical shifts in periodic systems based on gauge including atomic orbitals and density functional theory

2011 ◽  
Vol 89 (9) ◽  
pp. 1150-1161 ◽  
Author(s):  
Dmitry Skachkov ◽  
Mykhaylo Krykunov ◽  
Tom Ziegler
Keyword(s):  
Magnetic Field ◽  
Density Functional Theory ◽  
External Magnetic Field ◽  
Density Functional ◽  
Three Dimensional ◽  
Nuclear Magnetic Moment ◽  
Zero Order ◽  
Periodic Systems ◽  
Functional Theory ◽  
Atomic Orbitals

We report here on an improved first principles method that can determine NMR shielding tensors for periodic systems. Our scheme evaluates the shielding tensor as the second derivative of the total electronic energy with respect to a nuclear magnetic moment and an external magnetic field. Both the induced current density J(α) due to the first perturbation from the nuclear magnetic moment as well as the interaction of J(α) with the second perturbation in the form of an external magnetic field are evaluated analytically. Our approach is based on Kohn–Sham density functional theory and gauge-including atomic orbitals. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn–Sham potential fully without the use of effective core potentials. The method is implemented into the periodic program BAND. The new scheme represents an improvement over a previously proposed method in that use can be made of the zero-order Kohn–Sham orbitals from a calculation based on a primitive cell instead of a supercell. Further, J(α) is evaluated analytically rather than by a finite difference approach. The improvements reduce the required computational time by up to two orders of magnitude for three-dimensional systems. Such a reduction is made possible by the fact that we are using atomic centered basis functions. The new implementation is further able to take into account scalar relativistic effects within the zero-order regular approximation. Results from calculations of NMR shielding constants based on the present approach are presented for systems with one-, two-, and three-dimensional periodicity. The reported values are compared to experiment and results from the previously proposed scheme.

Electron density fitting for the Coulomb problem in relativistic density-functional theory

2006 ◽  
Vol 124 (12) ◽  
pp. 124104 ◽  
Author(s):  
Leonardo Belpassi ◽  
Francesco Tarantelli ◽  
Antonio Sgamellotti ◽  
Harry M. Quiney
Keyword(s):  
Density Functional Theory ◽  
Electron Density ◽  
Density Functional ◽  
Functional Theory ◽  
Coulomb Problem ◽  
Density Fitting
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