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- Variational_Monte_Carlo abstract "In mathematical physics, variational Monte Carlo (VMC) is a quantum Monte Carlo method that applies the variational method to approximate the ground state of the system.The expectation value necessary can be written in the representation as Following the Monte Carlo method for evaluating integrals, we can interpret as a probability distribution function, sample it, and evaluate the energy expectation value as the average of the local function , and minimize .VMC is no different from any other variational method, except that since the many-dimensional integrals are evaluated numerically, we only need to calculate the value of the possibly very complicated wave function, which gives a large amount of flexibility to the method. One of the largest gains in accuracy over writing the wave function separably comes from the introduction of the so-called Jastrow factor, where the wave function is written as , where is the distance between a pair of quantum particles. With this factor, we can explicitly account for particle-particle correlation, but the many-body integral becomes unseparable, so Monte Carlo is the only way to evaluate it efficiently. In chemical systems, slightly more sophisticated versions of this factor can obtain 80–90% of the correlation energy (see electronic correlation) with less than 30 parameters. In comparison, a configuration interaction calculation may require around 50,000 parameters to reach that accuracy, although it depends greatly on the particular case being considered. In addition, VMC usually scales as a small power of the number of particles in the simulation, usually something like N2−4 for calculation of the energy expectation value, depending on the form of the wave function.".
- Variational_Monte_Carlo wikiPageExternalLink 0409644.
- Variational_Monte_Carlo wikiPageExternalLink 0110003.
- Variational_Monte_Carlo wikiPageExternalLink 9911005.
- Variational_Monte_Carlo wikiPageExternalLink 1.
- Variational_Monte_Carlo wikiPageExternalLink 1.
- Variational_Monte_Carlo wikiPageExternalLink p3081.
- Variational_Monte_Carlo wikiPageExternalLink PhysRevB.72.085124.
- Variational_Monte_Carlo wikiPageExternalLink PhysRevLett.60.1719.
- Variational_Monte_Carlo wikiPageExternalLink pA442_1.
- Variational_Monte_Carlo wikiPageExternalLink p12344_1.
- Variational_Monte_Carlo wikiPageExternalLink p1173_1.
- Variational_Monte_Carlo wikiPageID "8987340".
- Variational_Monte_Carlo wikiPageRevisionID "597641773".
- Variational_Monte_Carlo hasPhotoCollection Variational_Monte_Carlo.
- Variational_Monte_Carlo subject Category:Mathematical_optimization.
- Variational_Monte_Carlo subject Category:Quantum_Monte_Carlo.
- Variational_Monte_Carlo subject Category:Quantum_chemistry.
- Variational_Monte_Carlo comment "In mathematical physics, variational Monte Carlo (VMC) is a quantum Monte Carlo method that applies the variational method to approximate the ground state of the system.The expectation value necessary can be written in the representation as Following the Monte Carlo method for evaluating integrals, we can interpret as a probability distribution function, sample it, and evaluate the energy expectation value as the average of the local function , and minimize .VMC is no different from any other variational method, except that since the many-dimensional integrals are evaluated numerically, we only need to calculate the value of the possibly very complicated wave function, which gives a large amount of flexibility to the method. ".
- Variational_Monte_Carlo label "Variational Monte Carlo".
- Variational_Monte_Carlo sameAs m.027sf0v.
- Variational_Monte_Carlo sameAs Q7915793.
- Variational_Monte_Carlo sameAs Q7915793.
- Variational_Monte_Carlo wasDerivedFrom Variational_Monte_Carlo?oldid=597641773.
- Variational_Monte_Carlo isPrimaryTopicOf Variational_Monte_Carlo.