Highly Accurate Random Phase Approximation Methods With Linear Time Complexity

95 Pages·2017·3.22 MB·English

by  Henry F. Schurkus

Dissertation zur Erlangung des Doktorgrades
der Fakulta¨t fu¨r Chemie und Pharmazie
der Ludwig-Maximilians-Universita¨t Mu¨nchen
Highly Accurate
Random Phase Approximation Methods
With
Linear Time Complexity
...
Henry Franz Schurkus
aus
Landshut
2017

Dissertation zur Erlangung des Doktorgrades
der Fakulta¨t fu¨r Chemie und Pharmazie
der Ludwig-Maximilians-Universita¨t Mu¨nchen
Highly Accurate
Random Phase Approximation Methods
With
Linear Time Complexity
Henry Franz Schurkus
aus
Landshut
2017

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Erkla¨rung
Diese Dissertation wurde im Sinne von 7 der Promotionsordnung vom 28. Novem-
§
ber 2011 von Herrn Prof. Dr. Christian Ochsenfeld betreut.
Eidesstattliche Versicherung
Diese Dissertation wurde eigensta¨ndig und ohne unerlaubte Hilfe erarbeitet.
Mu¨nchen,
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(Henry Schurkus)
Dissertation eingereicht am ...............0.7...0..7..2..0.1.7................
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Meinem Opa Franz-Josef Keite
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Summary
One of the key challenges of electronic structure theory is to find formulations to
compute electronic ground-state energies with high accuracy while being applicable
to a wide range of chemical problems. For systems beyond the few atom scale often
computations achieving higher accuracies than the so called double-hybrid density
functional approximations become prohibitively expensive. Here, the random phase
approximation,whichisknowntoyieldsuchhigheraccuracyresultshasbeendeveloped
from a theory applicable only to molecules on the tens of atoms scale into a highly
accurate and widely applicable theory. To this end, a mathematical understanding
has been developed that, without changing the computational complexity, allows to
eliminate the error introduced by the resolution-of-the-identity approximation which
had been introduced in the previous formulation. Furthermore, in this work a new
formulationoftherandomphaseapproximationformoleculeshasbeenpresentedwhich
achieves linear-scaling of compute time with molecular size—thereby expanding the
realm of molecules that can be treated on this level of theory to up to a thousand
atoms on a simple desktop computer. Finally, the theory has been matured to allow
foruseofevenextensivebasissetswithoutdrasticallyincreasingruntimes. Overall, the
presented theory is at least as accurate and even faster than the original formulation
for all molecules for which compute time is significant and opens new possibilities for
the highly accurate description of large quantum chemical systems.
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