  In this paper, we apply Ritz variational approach to a new isochemical model
of $H_2$ molecule suggested by Santilli and Shillady. We studied Gaussian,
$V_g$, and exponential, $V_e$, screened Coloumb potential {\it approximations},
as well as the original Hulten potential, $V_h$, case. Both the Coloumb and
exchange integrals have been calculated only for $V_e$ owing to Gegenbauer
expansion while for $V_g$ and $V_h$ cases we achieved analytical results only
for the Coloumb integrals. We conclude that the $V_e$-based model is capable to
fit experimental data on $H_2$ molecule in confirmation of the results of
numerical HFR approach by Santilli and Shillady. Also, we achieved the
energy-based estimation of the weight of the isoelectronium phase which is
appeared to be of the order of 1%...6%, for the case of $V_e$. However, we note
that this is {\it not} the result corresponding to the original
Santilli-Shillady model, which is based on the Hulten potential $V_h$. An
interesting result is that in order to prevent divergency of the Coloumb
integral for $V_h$ the correlation length parameter $r_c$ should run discrete
set of values. We used this condition in our $V_e$-based model.
