Local potential functional embedding theory: On the way towards quantum chemistry

Gulin, Martin Rafael (author), Fromager, Emmanuel (mentor), Podlipnik, Črtomir (co-mentor)

This master thesis describes an extension of a quantum embedding method called local potential functional embedding theory (LPFET). We have been able to find in-principle-exact connection between Kohn-Sham density functional theory (KS-DFT) and density matrix embedding theory (DMET), and based on this we have found a similar algorithm for more general, nonuniform model Hamiltonian operators (the Hubbard model). On the basis of this connection, we present a new embedding scheme with similar simplifications. The results shown in this work demonstrate that the generalized version of the LPFET successfully computes the electron density and energy of low- and medium-correlated systems. The newly developed extension of the method serves as a first step in extending the LPFET algorithm to applications in chemical ab initio Hamiltonian operators.

• Language: English
• Keywords: quantum chemistry, quantum embedding, Householder transformation, Hubbard model
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FKKT - Faculty of Chemistry and Chemical Technology
• Year: 2022
• PID: 20.500.12556/RUL-142819
• COBISS.SI-ID: 135280131
• Publication date in RUL: 28.11.2022

Secondary language

• Language: Slovenian
• Title: Teorija vložitve funkcionala lokalnega potenciala: Kvantni kemiji naproti

Abstract

Magistrsko delo opisuje razširitev metode kvantne vložitve imenovane teorija vložitve funkcionala lokalnega potenciala (LPFET). Uspeli smo najti teoterično eksaktno povezavo med Kohn-Shamovo teorijo gostotnega funkcionala (KS-DFT) ter teorijo vložitve s pomočjo gostotne matrike (DMET) in na podlagi tega najti podoben algoritem za splošnejše, nehomogene modelne Hamiltonove operatorje (Hubbardov model), na podlagi te povezave pa smo predstavili novo shemo vložitve s podobnimi poenostavitvami. Prikazani rezultati prikazujejo, da nadgrajena različica LPFET uspešno izračuna elektronsko gostoto ter energijo nizko in srednje koreliranih sistemov. Novonastala razširitev metode služi kot prvi korak razširitvi algoritma LPFET na uporabo v kemijskih ab initio Hamiltonovih operatorjih.

• Keywords: kvantna kemija, kvantna vdelava, Householderjeva transformacija, Hubbardov model