Multipole Moments of the Hydrogen Molecule

1975 ◽  
Vol 53 (19) ◽  
pp. 1781-1790 ◽  
Author(s):  
G. Karl ◽  
J. D. Poll ◽  
L. Wolniewicz
Keyword(s):  
Helium Atom ◽  
Internuclear Distance ◽  
Hydrogen Molecule ◽  
Hydrogen Gas ◽  
Multipole Moments ◽  
Vibrational States ◽  
Shielding Factor ◽  
Internuclear Distances ◽  
Variational Wave Functions ◽  
Variational Wave

For small internuclear distances, the quadrupole moment of the hydrogen molecule is quadratic in the internuclear distance, with a coefficient determined by the quadrupole shielding factor of the helium atom. Similarly the hexadecapole moment is quartic in the internuclear distance for small internuclear distances, with a coefficient which is determined by the properties of the helium atom. We give the results of a machine computation of the hexadecapole moment of the hydrogen molecule using up to 54 term variational wave functions and its matrix elements between rotational and vibrational states of the molecule. The intensity of the ΔJ = 4 induced spectrum of hydrogen gas is also discussed.

Variational energies for highly excited states of the helium atom

1978 ◽  
Vol 56 (6) ◽  
pp. 884-889 ◽  
Author(s):  
Wai-Tak Ma ◽  
Mary Kuriyan ◽  
Huw O. Pritchard
Keyword(s):  
Helium Atom ◽  
Excited States ◽  
Wave Functions ◽  
Experimental Results ◽  
New States ◽  
Variational Wave Functions ◽  
Variational Wave ◽  
S States

The efficient correlated variational wave functions used previously to study the higher 1 sns states of helium have been extended to other states of the helium atom, 1 snp (n ≤ 23), 2pnp1P (n ≤ 25), and 2pnp3P (n ≤ 25); similar uncorrelated wave functions were used for 1snd (n ≤ 21), 2pnp1D (n ≤ 10), and 2pnp3D (n ≤ 10). Attempts to use the same techniques for the 2pnp1,3S states appear to converge variationally to the energies of the 2s21S and 2s3s3S states respectively. Comparison is made with experimental results where appropriate, and agreement is excellent except in the case of the 1snd states above n = 13.A search was made for excited states of H− in each of these configurations, but no new states were found.

Polarizability and internuclear distance in the hydrogen molecule and molecule-ion

1950 ◽  
Vol 203 (1074) ◽  
pp. 364-374 ◽  
Keyword(s):  
Wave Function ◽  
Raman Scattering ◽  
Internuclear Distance ◽  
Hydrogen Molecule ◽  
Wave Functions ◽  
Fair Agreement ◽  
Equilibrium Internuclear Distance ◽  
Internuclear Distances

The polarizability of the hydrogen molecule-ion has been calculated for a range of internuclear distances, using various types of wave-functions. It is concluded that the values obtained for the polarizability are relatively insensitive to the choice of wave-function. Similar calculations have been made for the hydrogen molecule, using an LCAO wave-function. The value obtained for the polarizability at the equilibrium internuclear distance is in fair agreement with experiment and with the results of earlier calculations. The predicted variation of polarizability with internuclear distance agrees approximately with that deduced previously from the refractivities of hydrogen and deuterium, but is greater than that derived from the observed intnesities of Rayleigh and Raman scattering.

scholarly journals Numerical Calculation of Energy Eigen-values of the Hydrogen Negative Ion in the 2p^2 Configuration by Using the Variational Method

2020 ◽  
Vol 24 (1) ◽  
pp. 30
Author(s):  
Yosef Robertus Utomo ◽  
Guntur Maruto ◽  
Agung Bambang Setio Utomo ◽  
Pekik Nurwantoro ◽  
Sholihun Sholihun
Keyword(s):  
Numerical Calculation ◽  
Variational Method ◽  
Trial Function ◽  
Hydrogen Molecule ◽  
Negative Ion ◽  
Multipole Moments ◽  
A Value ◽  
Eigen Value ◽  
Eigen Values ◽  
Electric Multipole Moments

Calculation of energy eigen value of hydrogen negative ion (H − ) in 2p^2 configuration using the method of variation functions has been done. A work on H − can lead to calculations of electric multipole moments of a hydrogen molecule. The trial function is a linear combination of 8 expansion terms each of which is related to the Chandrasekhar’s basis. This work produces a series of 7 energy eigen values which converges to a value of −0.2468 whereas the value of this convergence is expected to be −0.2523. This deviation from the expected value is mainly due to the elimination of interelectronic distance (u) coordinate. The values of the exponent parameters used in this work contribute also to this deviation. This variational method will be applied to the construction of some energy eigen functions of Hv2 .

scholarly journals Improved variational wave functions for few-body nuclei

1995 ◽  
Author(s):  
R B Wiringa ◽  
A Arriaga ◽  
V R Pandharipande
Keyword(s):  
Wave Functions ◽  
Variational Wave Functions ◽  
Variational Wave

Interaction Potential between Ground State Helium Atom and theB1Σu+State of the Hydrogen Molecule

1972 ◽  
Vol 56 (3) ◽  
pp. 1219-1223 ◽  
Author(s):  
Henry F. Schaefer ◽  
Daniel Wallach ◽  
Charles F. Bender
Keyword(s):  
Helium Atom ◽  
Interaction Potential ◽  
Ground State ◽  
Hydrogen Molecule

Isotope Effect in Collision Between Helium Atom and Hydrogen Molecule

1998 ◽  
Vol 15 (1) ◽  
pp. 19-20 ◽  
Author(s):  
Xiang-dong Yang ◽  
Ji-yan Zhang ◽  
Fu-qian Jing
Keyword(s):  
Helium Atom ◽  
Isotope Effect ◽  
Hydrogen Molecule
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