Singlet–triplet gaps in diradicals obtained with diffusion quantum Monte Carlo using a Slater–Jastrow trial wavefunction with a minimum number of determinants

2019 ◽  
Vol 21 (36) ◽  
pp. 20422-20431 ◽  
Author(s):  
Xiaojun Zhou ◽  
Fan Wang
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Minimum Number ◽  
Trial Wavefunction

Reliable singlet–triplet gaps of diradicals are achieved with FN-DMC using the simplest ansatz for the trial wavefunction.

scholarly journals Diffusion and Reptation Quantum Monte Carlo Study of the NaK Molecule

2018 ◽  
Author(s):  
Marc E. Segovia ◽  
Oscar Ventura
Keyword(s):  
Monte Carlo ◽  
Dipole Moment ◽  
Potential Energy ◽  
Dissociation Energy ◽  
Quantum Monte Carlo ◽  
Density Functional ◽  
Basis Set ◽  
Energy Curve ◽  
Dft Methods ◽  
Trial Wavefunction

<p>Diffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree-Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance—interpolated from the potential energy curves—yield a value of 3.5 Å, in agreement with the experimental value. The dissociation energy, however, is not as good. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. On the contrary, the CCSD(T), other MO and DFT methods are not able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment. RMC methods are even better, and the value obtained with a B3LYP trial wavefunction is very close to the experimental one.</p>

MONTE CARLO STUDY OF ONE HOLE IN A QUANTUM ANTIFERROMAGNET

1992 ◽  
Vol 06 (05n06) ◽  
pp. 587-588
Author(s):  
S. Sorella
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Thermodynamic Limit ◽  
Quantum Monte Carlo ◽  
Finite Size ◽  
Monte Carlo Study ◽  
Mott Insulator ◽  
Trial Wavefunction ◽  
The One ◽  
Quantum Antiferromagnet

Using the standard Quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a Quantum Antiferromagnet. The calculation is very well stabilized, using selected sized systems and special use of the trial wavefunction that satisfy the “close shell condition” in presence of an arbitrarily weak Zeeman magnetic field, vanishing in the thermodynamic limit. It will be shown in a forthcoming publication1 that the presence of this magnetic field does not affect thermodynamic properties for the half filled system. Then I have used the same selected sizes for the one hole ground state. I have investigated the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator should behave just as conventional insulator with an upper and lower Hubbard band. By comparing the present finite size scaling with several techniques predicting a finite quasiparticle weight (see Fig.1) the data seem more consistent with a vanishing quasiparticle weight, i.e. , as recently suggested by P.W. Anderson2 the Hubbard-Mott insulator should be characterized by non-trivial excitations which cannot be interpreted in a simple quasi-particle picture. However it cannot be excluded , based only on numerical grounds, that a very small but non vanishing quasiparticle weight should survive in the thermodynamic limit.

Diffusion and Reptation Quantum Monte Carlo Study of the NaK Molecule

2018 ◽  
Author(s):  
Marc E. Segovia ◽  
Oscar Ventura
Keyword(s):  
Monte Carlo ◽  
Dipole Moment ◽  
Potential Energy ◽  
Dissociation Energy ◽  
Quantum Monte Carlo ◽  
Density Functional ◽  
Basis Set ◽  
Energy Curve ◽  
Dft Methods ◽  
Trial Wavefunction

<p>Diffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree-Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance—interpolated from the potential energy curves—yield a value of 3.5 Å, in agreement with the experimental value. The dissociation energy, however, is not as good. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. On the contrary, the CCSD(T), other MO and DFT methods are not able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment. RMC methods are even better, and the value obtained with a B3LYP trial wavefunction is very close to the experimental one.</p>

scholarly journals Using perturbatively selected configuration interaction in quantum Monte Carlo calculations

2013 ◽  
Vol 91 (9) ◽  
pp. 879-885 ◽  
Author(s):  
Emmanuel Giner ◽  
Anthony Scemama ◽  
Michel Caffarel
Keyword(s):  
Monte Carlo ◽  
Configuration Interaction ◽  
Quantum Monte Carlo ◽  
State Energy ◽  
Selection Process ◽  
Nonlinear Parameters ◽  
Nodal Structure ◽  
Trial Wavefunction ◽  
Fixed Node ◽  
Monte Carlo Framework

Defining accurate and compact trial wavefunctions leading to small statistical and fixed-node errors in quantum Monte Carlo (QMC) calculations is still a challenging problem. Here we propose to make use of selected configuration interaction (CI) expansions obtained by selecting the most important determinants through a perturbative criterion. A major advantage with respect to truncated CASSCF wavefunctions or CI expansions limited to a maximum number of excitations (e.g, CISD) is that much smaller expansions can be considered (many unessential determinants are avoided), an important practical point for efficient QMC calculations. The most important determinants entering first during the selection process (hierarchical construction) the main features of the nodal structure of the wavefunction can be expected to be obtained with a moderate number of determinants. Thanks to this property, the delicate problem of optimizing in a Monte Carlo framework the numerous linear and (or) nonlinear parameters of the determinantal part of the trial wavefunction could be avoided. As a first numerical example, the calculation of the ground-state energy of the oxygen atom is presented. The best DMC value reported so far is obtained.

Diffusion and Reptation Quantum Monte Carlo Study of the NaK Molecule

2018 ◽  
Author(s):  
Marc E. Segovia ◽  
Oscar Ventura
Keyword(s):  
Monte Carlo ◽  
Dipole Moment ◽  
Potential Energy ◽  
Dissociation Energy ◽  
Quantum Monte Carlo ◽  
Density Functional ◽  
Basis Set ◽  
Energy Curve ◽  
Dft Methods ◽  
Trial Wavefunction

<p>Diffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree-Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance—interpolated from the potential energy curves—yield a value of 3.5 Å, in agreement with the experimental value. The dissociation energy, however, is not as good. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. On the contrary, the CCSD(T), other MO and DFT methods are not able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment. RMC methods are even better, and the value obtained with a B3LYP trial wavefunction is very close to the experimental one.</p>

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