Applications of the fixed-node quantum Monte Carlo method
Başlık çevirisi mevcut değil.
- Tez No: 402015
- Danışmanlar: DR. LUBOS MITAS
- Tez Türü: Doktora
- Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2014
- Dil: İngilizce
- Üniversite: North Carolına State Unıversıty
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
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Özet (Çeviri)
Quantum Monte Carlo (QMC) is a highly sophisticated quantum many-body method. Diffusion Monte Carlo (DMC), a projected QMC method, is a stochastic solution of the stationary Schrödinger's equation. It is, in principle, an exact method. However, in dealing with fermions, since trial wave functions meet the antisymmetric condition of the many-body fermionic systems, it inevitably encounters the fermion sign problem. One of the ways to circumvent the sign problem is by imposing the so-called fixed-node approximation. The fixed-node DMC (FN-DMC), a highly promising method, is emerging as the method of choice for correlated treatment of many-body electronic structure problems since it is much more accurate than Khon-Sham DFT and has a competitive accuracy with CCSD(T) but scales better with system size than CCSD(T). An important drawback in FN-DMC is the fixed-node bias introduced by the approximate nature of the trial wave function nodes. In this dissertation, we examine the fixed-node bias and its restrictive impact on the accuracy of FN-DMC. Also, electron density dependence of the fixed-node bias is discussed by taking a relatively small atomic system. In our dissertation, we also applied FN-DMC in a relatively large molecular system with a transition metal, Zinc-porphyrin, to calculate the excitation energy in an adiabatic limit (vertical excitation). We found that FN-DMC results agree well with experimental values as well as with results obtained by some other correlated ab initio methods such as CCSD. In addition, we used FN-DMC to study a transition metal dimer, Mo2, which is a challenging system for theoretical studies since there is large amount of many-body correlation effects. We constructed the antisymmetric part (Slater part) of the trial wave function by means of the Selected-CI method. Moreover, we carried out CCSD(T) calculations in order to be able to compare FN-DMC energies with another correlated method energies. FN-DMC and CCSD(T) calculations in Mo2, which is dominant with d-d bondings, enabled us to make comparisons between these two competitive methods and investigate the limitations impairing FN-DMC accuracy.
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