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Explorations with ADF Amsterdam Density Functional. William Delfs Dr. Arlen Viste. What is Density Functional Theory?.
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Explorations with ADFAmsterdam Density Functional William Delfs Dr. Arlen Viste
What is Density Functional Theory? • DFT methods are based on the Hohenberg-Kohn theorem which states that the ground state electronic energy E of an atom or molecule can be expressed exactly as the electron density of the molecule. • Basically, by knowing the average density of electrons at all points in space, that is enough to uniquely determine the total energy [molecule], and therefore all of the other properties of the system.
Kohn • Kohn's 1965 publication, with Lu Sham of the University of California at San Diego, described a procedure for deriving the electron density and energy, based on solving equations for a corresponding system of non-interacting electrons (which is much easier to manage).
Kohn • The primary assumption here is that the energy and density functions are related, and this was proven in an earlier paper of Kohn’s (1964). • Walter Kohn and John Pople won the 1998 Nobel prize in chemistry for their advancement of computational chemistry.
What is “Functional?” • The term “functional” refers to the energy’s functional dependence on the density function. • Total electronic energy is: E = T + Vnucl + Vrep +EXC
Energies • E = T + Vnucl + Vrep +EXC • Vnucl = • Vrep = • From the above two equations for potential energies, the dependence on electron density is readily apparent.
Energies • VXC is the exchange-correlation potential. • Vxc is tied to LDA (Linear Density Approximation) for calculating the ground state and consequent excitation energies.
What is ADF? • The ADF package is software for first-principles electronic structure calculations. • Used everywhere from biochemistry to materials science. • Based on DFT, which has dominated computational chemistry since the early 1990’s. • Superior to HF and semi-empirical approaches. • It enables accurate treatment of larger systems than is capable by ab initio methods.
How it Works • ADF is used under a Linux operating system (UNIX based). • ADF is capable of parallel processing. • Uses a command line structure of Linux commands, as opposed to a window interface.
What ADF is Used for • The ADF package can be applied to isolated molecules, polymers, slabs, solids, molecules in solvents, and molecules in protein environments. • It can treat all elements of the periodic table and contains state of the art relativistic methods to treat heavy nuclei.
What ADF is Used for • ADF is especially suited for applications to transition metal compounds. • ADF can treat a wide range of molecular properties.
What we did with ADF • Focused on the relativistic capabilities of the software. • Studied Transition metal dimers such as Hg2+2, Au2, AuHg+, HgH+. • Unfortunately, it was only a small part of a very large and powerful package.
Relativistic Features • ADF supports the incorporation of relativistic effects in two ways. • Quasi-relativistic method based on the Pauli Hamiltonian. • The more recently developed zero-order regular approximation (ZORA).
Pauli Formalism vs. ZORA • The fundamental problem with Pauli Formalism is the absence of it being bound below. • It is necessary to use a frozen core (the lowest-lying molecular orbitals are constrained to remain doubly-occupied in all configurations) in combination with a limited (smaller) basis set.
ZORA • ZORA will generally give more accurate results, and can employ bigger basis sets. • The relativistic calculation is very similar in structure to a relativistic one, having only a few additional terms in the Hamiltonian.
How does ZORA do it? • The ZORA method is obtained by rewriting the energy expression. • Expand the E/(2mc2 – V) • Zeroth order term:
Acknowledgements • Dr. Arlen Viste • Augustana College Dept. of Chemistry • SCM Corporation for their provision of instrumental examples
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