scholarly journals A Note About the Ground State of the Hydrogen Molecule

2007 ◽  
Vol 72 (2) ◽  
pp. 164-170 ◽  
Author(s):  
Alexander V. Turbiner ◽  
Nicolais L. Guevara
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Trial Function ◽  
Hydrogen Molecule ◽  
State Energy ◽  
Variational Parameter ◽  
Electronic Correlation ◽  
Correlation Term

A trial function is presented for the H2 molecule which provides the most accurate (the lowest) Bohr-Oppenheimer ground state energy among few-parametric trial functions (with ≤14 parameters). It includes the electronic correlation term in the form ~ exp (γr12) where γ is a variational parameter.

Energy bounds for the spiked harmonic oscillator

1995 ◽  
Vol 73 (7-8) ◽  
pp. 493-496 ◽  
Author(s):  
Richard L. Hall ◽  
Nasser Saad
Keyword(s):  
Lower Bound ◽  
Harmonic Oscillator ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
Trial Function ◽  
State Energy ◽  
Parameter Range ◽  
Complementary Energy ◽  
Energy Bounds

A three-parameter variational trial function is used to determine an upper bound to the ground-state energy of the spiked harmonic-oscillator Hamiltonian [Formula: see text]. The entire parameter range λ > 0 and α ≥ 1 is treated in a single elementary formulation. The method of potential envelopes is also employed to derive a complementary energy lower bound formula valid for all the discrete eigenvalues.

scholarly journals Two-Parameter Harmonic Oscillator Expansion Method for Calculating Non-Relativistic Ground State Energy of Coulomb Three-Particle Systems with Two Identical Particles

2018 ◽  
Vol 173 ◽  
pp. 02006
Author(s):  
Algirdas Deveikis
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Traditional Approach ◽  
Coulomb Systems ◽  
Expansion Method ◽  
Variational Parameter ◽  
Oscillator Representation ◽  
Identical Particles ◽  
Oscillator Basis

The variational method in oscillator representation with individual parameters for each Jacobi coordinate is applied to the non-relativistic calculation of the ground state energy of a number of three-particle Coulomb systems, consisting of two identical particles and a different one. The accuracy and convergence rate of the calculations in the constructed oscillator basis are studied up to a total of 28 oscillator quanta. The results are compared with those of the traditional approach using only one such nonlinear variational parameter. The method with individual parameters for Jacobi coordinates is found to possess a number of advantages as compared to the traditional approach.

Comment on approximate molecular orbitals. III. The 1sσ and 2pπ states of HeH++

1968 ◽  
Vol 46 (14) ◽  
pp. 1647-1648 ◽  
Author(s):  
Robert L. Matcha ◽  
William D. Lyon ◽  
Joseph O. Hirschfelder
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Trial Function ◽  
State Energy ◽  
Molecular Orbitals ◽  
Perturbation Techniques ◽  
Perturbation Calculation

The results and conclusions of a recent paper by Cohen, McEachran, and McPhee concerning a perturbation calculation of the ground-state energy of HeH++ are compared with those found in an earlier paper by Matcha, Lyon, and Hirschfelder, which treated the same problem using essentially identical variation–perturbation techniques with a more general trial function.

THE ELECTRONIC CORRELATION EFFECT FROM WEAK TO STRONG IN THE THREE DIMENSIONAL ELECTRON GAS

2012 ◽  
Vol 26 (11) ◽  
pp. 1250065 ◽  
Author(s):  
ZHI-MING YU ◽  
QING-WEI WANG ◽  
YU-LIANG LIU
Keyword(s):  
Phase Transition ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Electron Gas ◽  
Three Dimensional ◽  
Positive Function ◽  
Correlation Effect ◽  
Electronic Correlation ◽  
The Difference

Based on the success of the eigenfunctional theory ( EFT) in the one-dimensional model,16,24,51 we apply it to the three-dimensional homogeneous electron gas. By EFT, we first present a rigorous expression of the pair distribution function g(r) of the electron gas. This expression effectively solves the negative problem of g(r) that when electronic correlation effect is strong, the previous theories give a negative g(r),9 while g(r) is strictly a positive function. From this reasonable g(r), we estimate and establish a newly effective fitting expression of the ground state energy of electron gas. The new fitting expression presents a similar result with present theories when rs is small, since only in the limit of rs is small, present theories estimate a exact ground state energy. When rs increases, the difference between EFT and other theories becomes more and more remarkable. The difference is expected as EFT estimates a reasonable g(r) and would effectively amend the overestimate of previous theories in the ground state energy. In addition, by the ground state energy, we estimate the phase transition derived by the strong correlation effect. When the density decreases, the electronic correlation effect changes from weak to strong and we observe a sudden phase transition from paramagnetic to full spin polarization occurring at rs = 31 ± 4.

Improved (1s)2 variational model for helium

Open Physics ◽  
2005 ◽  
Vol 3 (1) ◽  
pp. 1-7
Author(s):  
B. Reed
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Nuclear Charge ◽  
Variational Model ◽  
Variational Parameter ◽  
Effective Nuclear Charge ◽  
Upper Limit ◽  
Trial Wavefunction ◽  
Present Trial

AbstractThe ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e −γ(rA/a o)ne−γ(rB/a o)n. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 Eh (Eh=1 hartree) in comparison with the traditional (n=1) result of −2.84766 Eh. This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 Eh) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 Eh, the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy
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