Ground-state calculations of confined hydrogen molecule H2 using variational Monte Carlo method (original) (raw)
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Canadian Journal of Physics, 2016
The ground state energy of hydrogen molecular ion [Formula: see text] confined by a hard prolate spheroidal cavity is calculated. The case in which the nuclear positions are clamped at the foci is considered. Our calculations are based on using the variational Monte Carlo method with an accurate trial wave function depending on many variational parameters. The results were extended to also include the HeH++ molecular ion. The obtained results are in good agreement with the most recent results.
Ground State Calculations of the Confined Molecular Ions and Using Variational Monte Carlo Method
2015
Absract The ground state energy of hydrogen molecular ion confined by a hard prolate spheroidal cavity is calculated. The case in which the nuclear positions are clamped at the foci is considered. Our calculations are based on using the variational Monte Carlo method with an accurate trial wave function depending on many variational parameters. The calculations were extended also to include the molecular ion. The obtained results are in good agreement with the recent results.
Variational quantum monte carlo calculation of the ground state energy of hydrogen molecule
Bayero Journal of Pure and Applied Sciences, 2010
The ground state energy of the hydrogen molecule was numerically analysed using the quantum Monte Carlo (QMC) method. The type of QMC method used in this work is the Variational Quantum Monte Carlo [VQMC]. This analysis was done under the context of the accuracy of Born-Oppenheimer approximation [fixed nuclei restriction]. The ground state energies of Hydrogen molecule for different interproton separation ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 0 0. 1 4. 0 A are computed and compared with previous numerical and empirical results that are essentially exact. It has been found that the ground state energy of the hydrogen molecule obtained in this work approaches the precise value of-31.94eV.
A quantum Monte Carlo calculation of the ground state energy of the hydrogen molecule
The Journal of Chemical Physics, 1991
We have calculated the ground state energy of the hydrogen molecule using the quantum Monte Carlo (QMC) method of solving the Schrodinger equation, without the use of the Born-Oppenheimer or any other adiabatic approximations. The wave function sampling was carried out in the full 12-dimensional configuration space of the four particles (two electrons and two protons). Two different methods were employed: the diffusion quantum Monte Carlo (DQMC) method and the Green's function quantum Monte Carlo (GFQMC) method. This computation is very demanding because the configurations must be evolved on the time scale of the electronic motion, whereas the finite nuclear mass effects are resolved accurately only after equilibration on the much slower time scale of the nuclear motion. Thus, a very large number of iterations is required. The calculations were performed on the CM-2 Connection Machine computer, a massively parallel supercomputer. The enormous speedup afforded by the massive parallelism allowed us to complete the computation in a reasonable amount of time. The total energy from the DQMC calculations is -1.163 97 + 0.000 05 a.u. A more accurate result was obtained from the GFQMC calculations of -1.164 024 + 0.000 009 a.u. Expressed as a dissociation energy, the GFQMC result is 36 117.9 f 2.0 cm -', including the corrections for relativistic and radiative effects. This result is in close agreement with accurate nonadiabatic-relativistic dissociation energies from variational calculations (corrected for radiative effects) in the range of 36 117.9-36 118.1 cm-' and with the best experimentally determined dissociation energy of McCormack and Eyler 36 118.1 + 0.2 cm -'.
Application of variational Monte Carlo method to the confined helium atom
A new application of variational Monte Carlo method is presented to study the helium atom under the compression effect of a spherical box with radius (rc). The ground-state energies of the helium atom were calculated for different values of rc. Our calculations were extended to include Li+ and Be2+ ions. The calculations were based on the use of a compact accurate trial wave function with five variational parameters. To optimize variational parameters, we used the steepest descent method. The obtained results are in good agreement with previous results.
Molecular Physics, 2016
By Using the variational Monte Carlo (VMC) method, we calculate the 1 state energies, the dissociation energies and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0. . and 10. . The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of VMC method can be extended successfully to cover the case of molecules under the effect of the magnetic field.
By Using the variational Monte Carlo (VMC) method, we calculate the 1 state energies, the dissociation energies and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0 . . and 10 . . The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of VMC method can be extended successfully to cover the case of molecules under the effect of the magnetic field.
Physical Review E, 2008
The Lagrange-mesh method is an approximate variational calculation which resembles a mesh calculation because of the use of a Gauss quadrature. The hydrogen atom confined in a sphere is studied with Lagrange-Legendre basis functions vanishing at the center and surface of the sphere. For various confinement radii, accurate energies and mean radii are obtained with small numbers of mesh points, as well as dynamic dipole polarizabilities. The wave functions satisfy the cusp condition with 11-digit accuracy.
Quantum computing simulation of the hydrogen molecular ground-state energies with limited resources
Open Physics
In this article, the hydrogen molecular ground-state energies using our algorithm based on quantum variational principle are calculated. They are calculated through a simulator since the system of the present study (i.e., the hydrogen molecule) is relatively small and hence the ground-state energies for this molecule are efficiently classically simulable using a simulator. Complete details of this algorithm are elucidated. For this, a full description on the fermions–qubits and the molecular Hamiltonian–qubit Hamiltonian transformations, is given. The authors search for qubit system parameters ( θ 0 {\theta }_{0} and θ 1 {\theta }_{1} ) that yield the minimum energies for the system and also study the ground state energies as a function of the molecular bond length. Proposed circuit is humble and does not include many parameters compared with that of Kandala et al., the authors control only two parameters ( θ 0 {\theta }_{0} and θ 1 {\theta }_{1} ).
A study of the confined hydrogen atom using the finite element method
Journal of Physics B: Atomic, Molecular and Optical Physics, 2005
The hydrogen atom confined by an infinite spherical potential barrier is studied employing a variational procedure based on the p-version of the finite element method. In such a procedure, the spherical spatial confinement is imposed straightforwardly by removing a local basis function. The calculations have been performed for estimating the energy spectrum, the dipole polarizability and the effective pressure for various confinement radii. The effect of the spatial confinement on these quantities is analysed. The results obtained are compared with those previously published in the literature and the efficiency of the finite element method to treat confined quantum systems is discussed.