Towards Correlated Sampling for the Fixed-Node Diffusion Quantum Monte Carlo Method
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Raphael Berner
Most methods of quantum chemistry calculate total energies rather than directly the energy differences that are of interest to chemists. In the case of statistical methods like quantum Monte Carlo the statistical errors in the absolute values need to be considerably smaller than their difference. The calculation of small energy differences is therefore particularly time consuming. Correlated sampling techniques provide the possibility to compute directly energy differences by simulating the underlying systems with the same stochastic process. The smaller the energy difference the smaller its statistical error. Correlated sampling is well established in variational quantum Monte Carlo, but it is much more difficult to implement in diffusion quantum Monte Carlo because of the fixed node approximation. A correlated sampling formalism and a corresponding algorithm based on a transformed Schrödinger equation having the form of a Kolmogorov’s backward equation is derived. The numerical verification of the presented algorithm is given for the harmonic oscillator. The extension of the algorithm to electron structure calculations is discussed.
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Artikel in diesem Heft
- Dedicated Editorial Communication: Jörg Fleischhauer 75
- Towards Correlated Sampling for the Fixed-Node Diffusion Quantum Monte Carlo Method
- Maxwell’s Demon Observing Creation of a Molecular Vibration
- Electronic and Magnetic Properties of the Graphene/Eu/Ni(111) Hybrid System
- The Conformation of Pentanoates in the Solid and in the Gas Phase
- The Role of Heme Chirality in the Circular Dichroism of Heme Proteins
- Convenient Small-Scale Preparation of p-Carborane by Pyrolysis of o-Carborane
- Computational Study of the Structure, the Flexibility, and the Electronic Circular Dichroism of Staurosporine – a Powerful Protein Kinase Inhibitor
- Quantum-Chemical Investigations on the Structural Variability of Anion–π Interactions
- Quantum-Chemical Ab Initio Calculations on Ala-(C5H5Al) and Galabenzene (C5H5Ga)
- A Short Review on the Magnetic Effects Occurring at Organic Ferromagnetic Interfaces Formed between Benzene-Like Molecules and Graphene with Ferromagnetic Surfaces
- Theoretical Analysis of the Unusual Vicinal Effects on Electronic Circular Dichroism Spectra of Cobalt(III) Complexes with ED3A-Type and Related Ligands
- Bonding Situation in Dimeric Group 15 Complexes [(NHC)2(E2)] (E = N–Bi)
Artikel in diesem Heft
- Dedicated Editorial Communication: Jörg Fleischhauer 75
- Towards Correlated Sampling for the Fixed-Node Diffusion Quantum Monte Carlo Method
- Maxwell’s Demon Observing Creation of a Molecular Vibration
- Electronic and Magnetic Properties of the Graphene/Eu/Ni(111) Hybrid System
- The Conformation of Pentanoates in the Solid and in the Gas Phase
- The Role of Heme Chirality in the Circular Dichroism of Heme Proteins
- Convenient Small-Scale Preparation of p-Carborane by Pyrolysis of o-Carborane
- Computational Study of the Structure, the Flexibility, and the Electronic Circular Dichroism of Staurosporine – a Powerful Protein Kinase Inhibitor
- Quantum-Chemical Investigations on the Structural Variability of Anion–π Interactions
- Quantum-Chemical Ab Initio Calculations on Ala-(C5H5Al) and Galabenzene (C5H5Ga)
- A Short Review on the Magnetic Effects Occurring at Organic Ferromagnetic Interfaces Formed between Benzene-Like Molecules and Graphene with Ferromagnetic Surfaces
- Theoretical Analysis of the Unusual Vicinal Effects on Electronic Circular Dichroism Spectra of Cobalt(III) Complexes with ED3A-Type and Related Ligands
- Bonding Situation in Dimeric Group 15 Complexes [(NHC)2(E2)] (E = N–Bi)
