Quantum Monte Carlo, Or, Solving the Many‐Particle Schrödinger Equation Accurately While Retaining Favorable Scaling with System Size

Towler, M. D.

doi:10.1002/9780470930779.ch4

Cited by 8 publications

(9 citation statements)

References 143 publications

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“…In this work the Fixed-Node Diffusion Monte Carlo (FN-DMC) method -the standard quantum Monte Carlo electronic-structure approach for molecules-is employed. For a detailed presentation of its theoretical and practical aspects, the reader is referred to the literature, e.g [1,21,22]. Here, we just recall that the central quantity of such approaches is the trial wavefunction Ψ T determining both the magnitude of the fixed-node error through its approximate nodes as discussed in the introduction and the quality of the statistical convergence (good trial wavefunctions = small statistical fluctuations).…”

Section: The Fixed-node Diffusion Monte Carlomentioning

confidence: 99%

“…Actually, it is not true since in the spin-free formalism used in QMC (Ref. [23] and also [1,21,22]) each Slater determinant expressed in terms of spin-orbitals decomposes into a product of two determinants, each of them corresponding to a given occupation of a set of purely spatial molecular orbitals. In practice, only two inverse Slater matrices (one of each spin) are computed with an O(N 3 ) algorithm.…”

Section: The Fixed-node Diffusion Monte Carlomentioning

confidence: 99%

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Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

Giner

Scemama

Caffarel

2015

The Journal of Chemical Physics

101

128

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The potential energy curve of the F2 molecule is calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction (CI)-type trial wavefunctions. To keep the number of determinants reasonable (the first and second derivatives of the trial wavefunction need to be calculated at each step of FN-DMC), the CI expansion is restricted to those determinants that contribute the most to the total energy. The selection of the determinants is made using the socalled CIPSI approach (Configuration Interaction using a Perturbative Selection made Iteratively). Quite remarkably, the nodes of CIPSI wavefunctions are found to be systematically improved when increasing the number of selected determinants. To reduce the non-parallelism error of the potential energy curve a scheme based on the use of a R-dependent number of determinants is introduced. Numerical results show that improved FN-DMC energy curves for the F2 molecule are obtained when employing CIPSI trial wavefunctions. Using the Dunning's cc-pVDZ basis set the FN-DMC energy curve is of a quality similar to that obtained with FCI/cc-pVQZ. A key advantage of using selected CI in FN-DMC is the possibility of improving nodes in a systematic and automatic way without resorting to a preliminary multi-parameter stochastic optimization of the trial wavefunction performed at the Variational Monte Carlo level as usually done in FN-DMC.

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Section: The Fixed-node Diffusion Monte Carlomentioning

confidence: 99%

Section: The Fixed-node Diffusion Monte Carlomentioning

confidence: 99%

Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

Giner

Scemama

Caffarel

2015

The Journal of Chemical Physics

101

128

View full text Add to dashboard Cite

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“…() is considerably more complex than the traditional classical MC approach and would require the band structure and electron wave‐functions of the material under study. The Bohmian Quantum Trajectory method is more usually used for Quantum Molecular Dynamics or Quantum Hydrodynamic calculations (Towler, ). The Quantum MC (QMC) program CASINO which is used, for example, to carry out Quantum chemistry calculations (Towler, ) (not to be confused with the electron transport simulation program of the same name (Demers et al ., ) uses the Quantum Trajectory method.…”

Section: Introducing Quantum Mechanics To Monte Carlo Simulationsmentioning

confidence: 99%

“…The Bohmian Quantum Trajectory method is more usually used for Quantum Molecular Dynamics or Quantum Hydrodynamic calculations (Towler, ). The Quantum MC (QMC) program CASINO which is used, for example, to carry out Quantum chemistry calculations (Towler, ) (not to be confused with the electron transport simulation program of the same name (Demers et al ., ) uses the Quantum Trajectory method. Pseudo potential methods of DFT cannot be used to simulate high energy electrons as these will penetrate into the inner core of atoms due to the use of pseudo‐potentials and this is where the DFT programs make their approximations.…”

Section: Introducing Quantum Mechanics To Monte Carlo Simulationsmentioning

confidence: 99%

“…The more computationally expensive Full Potential methods would need to be used instead. Pseudopotentials have also been employed in QMC to speed up calculations (Towler, ), but care in their use for electron transport simulations needs to be taken. Ruan et al ., ) based their method on the well‐known TEM multi‐slice method and so high angle elastic scattering effects can be ignored.…”

Section: Introducing Quantum Mechanics To Monte Carlo Simulationsmentioning

confidence: 99%

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Simulations and measurements in scanning electron microscopes at low electron energy

2016

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Summary: The advent of new imaging technologies in Scanning Electron Microscopy (SEM) using low energy (0-2 keV) electrons has brought about new ways to study materials at the nanoscale. It also brings new challenges in terms of understanding electron transport at these energies. In addition, reduction in energy has brought new contrast mechanisms producing images that are sometimes difficult to interpret. This is increasing the push for simulation tools, in particular for low impact energies of electrons. The use of Monte Carlo calculations to simulate the transport of electrons in materials has been undertaken by many authors for several decades. However, inaccuracies associated with the Monte Carlo technique start to grow as the energy is reduced. This is not simply associated with inaccuracies in the knowledge of the scattering cross-sections, but is fundamental to the Monte Carlo technique itself. This is because effects due to the wave nature of the electron and the energy band structure of the target above the vacuum energy level become important and these are properties which are difficult to handle using the Monte Carlo method. In this review we briefly describe the new techniques of scanning low energy electron microscopy and then outline the problems and challenges of trying to understand and quantify the signals that are obtained. The effects of charging and spin polarised measurement are also briefly explored. SCANNING 9999:1-17, 2016.

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Quantum monte carlo study of the retinal minimal model C₅H₆NH₂⁺

Coccia

Guidoni

2012

J Comput Chem

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In this work, we study the electronic and geometrical properties of the ground state of the Retinal Minimal Model C(5)H(6)NH(2)(+) using the variational Monte Carlo (VMC) method by means of the Jastrow antisymmetrized geminal power (JAGP) wavefunction. A full optimization of all wavefunction parameters, including coefficients, and exponents of the atomic basis, has been achieved, giving converged geometries with a compact and correlated wavefunction. The relaxed geometries of the cis and trans isomers present a pronounced bond length alternation pattern characterized by a C=C central double bond slightly shorter than that reported by the CASPT2 structures. The comparison between different basis sets indicates converged values of geometrical parameters, energy differences, and dipole moments even when the smallest wavefunction is used. The compactness of the wavefunction as well as the scalability of VMC optimization algorithms on massively parallel computers opens the way to perform full structural optimizations of conjugated biomolecules of hundreds of electrons by correlated methods like Quantum Monte Carlo.

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Quantum Monte Carlo, Or, Solving the Many‐Particle Schrödinger Equation Accurately While Retaining Favorable Scaling with System Size

Cited by 8 publications

References 143 publications

Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

Simulations and measurements in scanning electron microscopes at low electron energy

Quantum monte carlo study of the retinal minimal model C₅H₆NH₂⁺

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Quantum Monte Carlo, Or, Solving the Many‐Particle Schrödinger Equation Accurately While Retaining Favorable Scaling with System Size

Cited by 8 publications

References 143 publications

Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

Simulations and measurements in scanning electron microscopes at low electron energy

Quantum monte carlo study of the retinal minimal model C5H6NH2+

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Product

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Quantum monte carlo study of the retinal minimal model C₅H₆NH₂⁺