Solid hydrogen and deuterium. II. Pressure and compressibility calculated by a lowest-order constrained-variation method

1988 ◽  
Vol 71 (5-6) ◽  
pp. 341-349
Author(s):  
Geir Pettersen ◽  
Erlend �stgaard
Keyword(s):  
Solid Hydrogen ◽  
Variation Method ◽  
Constrained Variation

Spin-polarized hydrogen, deuterium, and tritium: I. Ground-state energy calculated by a lowest order constrained-variation method

1989 ◽  
Vol 67 (1) ◽  
pp. 63-71 ◽  
Author(s):  
Magne Haugen ◽  
Erlend Østgaard
Keyword(s):  
Binding Energy ◽  
Molar Volume ◽  
Ground State ◽  
Particle Density ◽  
Variation Method ◽  
Ground State Binding Energy ◽  
Spin Polarized ◽  
Hydrogen Deuterium ◽  
Constrained Variation ◽  
Theoretical Results

The ground-state energy of spin-polarized hydrogen, deuterium, and tritium is calculated by means of a modified variational lowest order constrained-variation method, and the calculations are done for five different two-body potentials. Spin-polarized H↓ is not self-bound according to our theoretical results for the ground-state binding energy. For spin-polarized D↓, however, we obtain theoretical results for the ground-state binding energy per particle from −0.42 K at an equilibrium particle density of 0.25 σ−3 or a molar volume of 121 cm3/mol to + 0.32 K at an equilibrium particle density of 0.21 σ−3 or a molar volume of 142 cm3/mol, where σ = 3.69 Å (1 Å = 10−10 m). It is, therefore, not clear whether spin-polarized deuterium should be self-bound or not. For spin-polarized T↓, we obtain theoretical results for the ground-state binding energy per particle from −4.73 K at an equilibrium particle density of 0.41 σ−3 or a molar volume of 74 cm3/mol to −1.21 K at an equilibrium particle density of 0.28 σ−3 or a molar volume of 109 cm3/mol.

Spin-polarized hydrogen, deuterium, and tritium: II. Pressure and compressibility calculated by a lowest order constrained-variation method

1989 ◽  
Vol 67 (7) ◽  
pp. 649-656 ◽  
Author(s):  
Magne Haugen ◽  
Erlend Østgaard
Keyword(s):  
Molar Volume ◽  
Ground State ◽  
Particle Density ◽  
Variation Method ◽  
Density Region ◽  
Spin Polarized ◽  
Hydrogen Deuterium ◽  
Constrained Variation ◽  
Ground State Energies ◽  
Theoretical Results

The pressure and the compressibility of spin-polarized H↓, D↓, and T↓ are obtained from ground-state energies calculated by means of a modified variational lowest order constrained-variation method. The pressure and the compressibility are calculated or estimated from the dependence of the ground-state energy on density or molar volume, generally in a density region from 0 to 1.5σ−3 corresponding to a molar volume of more than 20 cm3/mol, where σ = 3.69 Å (1Å = 10−10 m); the calculations are done for five different two-body potentials. Theoretical results for the pressure are 54.1–57.9 atm for spin-polarized H↓ 18.4–23.4 atm for spin-plolarized D↓, and 5.6–12.9 atm for spin-polarized T↓ at a particle density of 0.50σ−3 or a molar volume of 60 cm3/mol (1 atm = 101 kPa). Theoretical results for the compressibility are 51 × 10−4 −54 × 10−4 atm−1 for spin-polarized H↓, 108 × 10−4 −120 × 10−4 atm−1 for spin-polarized D↓, and 162 × 10−4 −224 × 10−4 atm−1 for spin-polarized T↓ at a particle density of 0.50σ−3 for a molar volume of 60 cm3/mol. The relative agreement between results for different potentials is somewhat better for higher densities.

Constrained variation method for excited‐state energies of atoms and molecules

1973 ◽  
Vol 59 (4) ◽  
pp. 1721-1725 ◽  
Author(s):  
P. S. C. Wang ◽  
Margaret Lowe Benston ◽  
D. P. Chong
Keyword(s):  
Excited State ◽  
Variation Method ◽  
Atoms And Molecules ◽  
Constrained Variation
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