Interaction energies for the H-H (sub 2) and H (sub 2) - H (sub 2) systems have been obtained by a semi-empirical perfect-pairing procedure used previously. The results have been compared with interaction energies obtained from other sources and the agreement among the different curves is reasonably good. A brief discussion of the previous applications of this semi-empirical scheme to other systems is included

Mason, Edward A.

Vanderslice, Joseph T.

NASA Technical Reports Server

N93361 
Interaction Energies for the H-H 2
 and H 2-H 2 System 
JOSEPH T. VANDERSLICE AND EDWARD A. MASON 
LTRY COPY 
MAR 
Reprinted from ThE JOURNAL OF CHEMICAL PHYSICS, Vol. 33, No. 2, Pages 492-494, August, 1960
https://ntrs.nasa.gov/search.jsp?R=20150020879 2019-08-31T05:35:50+00:00Z
Interaction Energies for the H-112'and H 2-H 2 System* 
JOSEPH T. VANDERSLICE AND EDWARD A. MASON	 '.	 :	 . 
Inslilule for Molecular Physics, University of Maryland, College Park, Maryland 
(Received March 3, 1960) 
Interaction energies for the H H, and H,-H2
 systems have been obtained by a semiempirical perfect 
pairing procedure used previously. The results have been compàred withinteraction energies obtained frOm 
other sources and the agreement among the different curves is reasonably good; A brief discussion of the 
previous apphcations of this semiempirical scheme to other systems is included. 
INTRODUCTION another, they can interact along ei jher one of two 
A CALCULATION of the transport properties of a potential curves, corresponding to the 	 and 
Li gas presupposes a knowledge of the interaction spectroscopic states of molecular hydrogen. Reasonably 
energies between the various species present in the gas accurate curves for these interactions are known,25 
Hydrogen gas at temperatures of several thousand but the curves for the interactions such as H-H 2 and 
degrees will contain not only hydrogen molecules but H2-H2 are not well known over a range' "of distance 
also a fair amount of ground-state hydrogen atoms, corresponding to interaction energies of about a volt or 
Consequently, the atom-atom, atom-molecule,
	 and less. This latter range, is the important one iii deter-
molecule-molecule interactions must be known if one mining high temperature properties 
wants to obtain reliable results from a transport- - Previously we have used the valence-bond scheme of 
property calculation	 Hydrogen should serve as a perfect pairing6 to generate atom molecule and mole 
particularly simple example for the calculation of j. T. Vanderslice, E. A Mason, W. G. Maisch and E R 
transport properties of hot gases, and its transport Lippincott, J
.
 Mol. Spectroscopy 3, 17(1959). 	 , 
properties are of some current interest for their own .	 'H. M. 'ames, A. S. Coolidge,' and R. D. Presnt, J; Chem. 
. 
sa.e.
Phys.4,18	 (1936).	 ,	 '	 .	 .. 
k. Dalgarno and N. Lynn, Proc. Phys. Soc. (London) A69, 
As two ground-state hydrogen atoms approach one 821	 (1956).	 .'...' 
'R. J
.
 Fallon, E. A.. Mason and. J
.
 T. Vanderslice, Astrophys. 
* This research was supported in part by the National Aero- J. 131, 12 (1960).	 ' 
nautics and Space Administration. 	 ' C. A. Coulson,. Valence (Oxford University Press; London, 
I J• J Newgard and M. Levoy, Sci. American 200, 46 (1959). 1952), pp. 166-171.
ti 
493	 INTERACTION ENERGIES FOR H-H 2 AND H2-H2 
cule-molecule interactions from a knowledge of atom-
atom interactions. The results so obtained agreed well 
with the available experimental data. 7 '° It seemed 
reasonable to suppose that we might use the same 
semiempirical procedure to calculate the interaction 
energies for the H-H2
 and H2-H2 systems from a knowl-
edge of the H-H interactions. These systems also serve 
as an especially simple case for the further testing of 
this semiempirical scheme. Curves for these interac-
tions have been obtained and are compared with results 
obtained by other methods. 
METHOD AND RESULTS 
The perfect-pairing procedure yields for the interac-
tion energy of a system6 
v=	 (1) 
paired	 nonpaired	 orbitals with 
orbitals	 orbitals	 parallel spins 
if one neglects Coulombic terms which should be small 
at large distances. Here J 1 is the exchange integral 
involving the orbitals I andj. Equation (1) immediately 
yields for the interaction energies between two ground-
state H atoms
V(')=+J, 
V(3 )=—J.	 (2) 
For the interaction between H atoms in different 
molecules, however, where spins are randomly oriented 
with respect to one another, one obtains 
V(H...H)=—J.	 (3) 
Following the procedure we have used in the past,7° 
we evaluated J from a knowledge of the interaction 
curve for the state, and used this same J to obtain 
>
R(A) 
FIG. 1. Interaction energies for the H-H2
 system. The curve 
indicated by Eq. (5) was calculated by the perfect-pairing pro-
cedure. The two curves at larger distances are Margenau's calcu-
lated curves for the linear and triangular configurations, the 
upper curve being due to the linear one. The circle corresponds 
to a point on the H-H2 curve obtained from scattering data on 
the H—H2 system. 
7 J. T. Vanderslice, E. A. Mason, and E. R. Lippincott, J. 
Chem. Phys. 30, 129 (1959). 
8 J. T. Vanderslice, E. A. Mason, and W. G. Maisch, J . Chem. 
Phys. 31, 738 (1959). 
J . T. Vanderslice, E. A. Mason, and W. G. Maisch, J . Chem. 
Phys. 32, 515 (1960). 
1O J . T. Vanderslice and E. A. Mason, Revs. Modern Phys. 32, 
417 (1960).
> 
5 
>
aCoSIty 
R(4) 
FIG. 2. Interaction energies for the 112-H2 system. The curve 
indicated by Eq. (6) was calculated by the perfect-pairing pro-
cedure. The curve marked "viscosity" was obtained from high-
temperature viscosity measurements. The dashed part of this 
latter curve is an extrapolation. The circles are Evett and Mar-
genau's calculated results. 
V(H . . .H) by Eq. (3). We have taken the expression 
for V( 3 ) from footnote reference 5. This yields 
V(H . •H) =30.21e_3 °1 ev,	 0.8 A<r<2.1 A. (4) 
The interaction between an atom and a molecule or 
between molecules is then, consistent with the perfect-
pairing approximation, just the sum of all the separate 
interactions. The results of course depend on the rela-
tive orientations of the approaching species. Many 
times, it is useful to have potentials averaged over 
orientations for purposes of comparison with experi-
mental results. The methods of averaging have been 
summarized previously for cases where all orientations 
are equally probable.7 Application of this procedure 
gives for the H-H2 interaction, 
(V(R) )=61.5e_29 ev,	 0.86 A<R<2.12 A, (5)
and for the 112-H2 interaction, 
(V(R))= 116.529R ev,	 0.91 A<R<2.14 A, (6) 
where R is the distance between the centers of mass of 
the species. 
These curves are plotted in Figs. 1 and 2, respec-
tively. The H-H2 curve can be compared with the first-
order perturbation results of Margenau, 11 who cal-
culated the interaction energy for both the linear and 
triangular cases. His results are shown in Fig. 1. Equa-
tion (5) can also be compared with one point (indicated 
by the circle in Fig. 1) on the H-H2
 curve obtained 
indirectly from the scattering of H ions in H2. It is 
seen to fall below the curve given by Eq. (5). There are 
two likely reasons for this. First, this point is not 
unambiguously determined because of the difficulty 
in interpreting the experimental results.0 Secondly, 
our averaging assumes that all orientations are equally 
probable, which is certainly not the case at distances of 
the order of 1 A. 
The H2-H2 potential can be compared at larger dis-
1 H. Margenau, Phys. Rev. 66, 303 (1944); 64, 131 (1943). 
' E. A. Mason and J
.
 T. Vanderslice, J
.
 Chem. Phys. 28, 1070 
(1958).


Interaction Energies for the H-H (sub 2) and H (sub 2) - H (sub 2) System

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