Screened exchange corrections to the random phase approximation from many-body perturbation theory

The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms, which would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of Second Order Screened Exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as $\mathcal O(N^5)$ or $\mathcal O(N^4)$ in orbital space or real space, respectively. Its memory requirement scales as $\mathcal O(N^2)$

A Full Configuration Interaction Perspective on the Homogeneous Electron Gas

Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a newly developed stochastic technique, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction expanded in plane wave Slater determinants. Despite the introduction of a basis set incompleteness error, we obtain a finite-basis energy which is significantly, and variationally lower than any previously published work for the 54-electron HEG at $r_s$ = 0.5 a.u., in a Hilbert space of $10^{108}$ Slater determinants. At this value of $r_s$, as well as of 1.0 a.u., we remove the remaining basis set incompleteness error by extrapolation, yielding results comparable or better than state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in sizable periodic systems.Comment: 4-page lette

Diagrammatic techniques for extended systems

Diese Doktorarbeit befasst sich mit der Implementierung und Evaluierung von drei wellenfunktionsbasierten Methoden für Festkörper unter periodischen Randbedingungen: (i) Zweite Ordnung Møller-Plesset Störungstheorie (MP2), (ii) Random phase approximation plus second-order screened exchange (RPA+SOSEX), und (iii) Coupled-cluster singles and doubles (CCSD). Der erste Teil erklärt die verwendeten theoretischen sowie computerorientierten Methoden. Die implementierten Ausdrücke der Hartree-Fock, MP2, RPA+SOSEX und CCSD theorien werden teilweise abgeleitet. Natural orbitals werden eingeführt und auf der Ebene von MP2 approximiert. Ausserdem wird die Berechnung der benötigten Ausdrücke im Rahmen der projector-augmented wave (PAW) Methode, welche im Vienna ab-initio simulation package (VASP) implementiert ist, erörtert. Der zweite Teil beinhaltet die numerischen Ergebnisse der verschiedenen Methoden und deren Interpretation. Gitterkonstanten, Bulkmoduli, Atomsierungsenergien und Quasiteilchen Bandlücken wurden mit Hilfe von HF und MP2 für eine Serie von Halbleitern und Isolatoren berechnet. Wir zeigen dass MP2 stark abschirmende Materialien überkorreliert und schwach abschirmende Materialien unterkorreliert. Dies führt zu einer Über- bzw. Unterschätzung von Gitterkonstanten für schwach bzw. stark abschirmende Materialien. RPA+SOSEX wurde verwendet um totale Korrelationsenergien von Atomen, Atomisierungsenergien von kleinen Molekülen, sowie Gitterkonstanten und Atomisierungsenergien von Halbleitern und Isolatoren zu berechnen. Es wird gezeigt das die Berücksichtigung von SOSEX mehrere Probleme der RPA löst. Insbesondere korrigiert SOSEX die Tendenz der RPA zur Unterschätzung von Bindungsenergien und Überschätzung von totalen Korrelationsenergien. Schlussendlich wird die CCSD Implementierung mit Hilfe von MP2 natural orbitals für das LiH Molekül und den LiH Festkörper getestet. Die CCSD Ergebnisse stimmen gut mit quantenchemischen Berechnungen überein.This thesis is devoted to the implementation and assessment of three wave function based methods for solid state systems under periodic boundary conditions: (i) Second-order Møller-Plesset perturbation theory (MP2), (ii) Random phase approximation plus second-order screened exchange (RPA+SOSEX), and (iii) Coupled-cluster singles and doubles (CCSD). The first part briefly reviews the employed theoretical and computational methods. The implemented expressions of the Hartree-Fock, MP2, RPA+SOSEX and CCSD theories are derived. Natural orbitals are introduced and approximated at the level of MP2. Moreover, we explain the evaluation of the required quantities in the framework of the projector-augmented wave (PAW) method as implemented in the Vienna ab-initio simulation package (VASP). The second part summarizes the results that have been obtained at the different levels of theory. Structural properties, atomization energies and quasiparticle band gaps have been calculated using HF and MP2 for archetypical semiconductors and insulators. It is shown that MP2 tends to overcorrelate strongly screening materials and undercorrelate weakly screening materials. This leads to an over- and underestimation of lattice constants for weakly and strongly screening materials, respectively. The RPA+SOSEX method was employed for the evaluation of total correlation energies of atoms, atomization energies of small molecules, as well as lattice constants and atomization energies of a series of semiconductors and insulators. We show that the introduction of second-order screened exchange lifts some deficiancies of the RPA, such as the underbinding of molecules and solids, and the overestimation of the total correlation energies. Finally, using CCSD and MP2 natural orbitals our CCSD implementation was tested for the LiH molecule as well as solid. Our results agree very well with results that have been obtained using quantum chemical codes

Averting the infrared catastrophe in the gold standard of quantum chemistry

Coupled-cluster theories can be used to compute ab initio electronic correlation energies of real materials with systematically improvable accuracy. However, the widely-used coupled cluster singles and doubles plus perturbative triples (CCSD(T)) method is only applicable to insulating materials. For zero-gap materials the truncation of the underlying many-body perturbation expansion leads to an infrared catastrophe. Here, we present a novel perturbative triples formalism that yields convergent correlation energies in metallic systems. Furthermore, the computed correlation energies for the three dimensional uniform electron gas at metallic densities are in good agreement with quantum Monte Carlo results. At the same time the newly proposed method retains all desirable properties of CCSD(T) such as its accuracy for insulating systems as well as its low computational cost compared to a full inclusion of the triples. This paves the way for ab initio calculations of real metals with chemical accuracy.Comment: 6 pages, 1 figure, 1 table plus a supplemental material of 14 pages, 4 figures and 1 tabl