Internuclear potential energy (electronic energy including internuclear
  repulsion) for hydrogen molecular monovalent cation ground state
 (Calculation of the same for the first excited states is too error-prone)

  Formulae used (Quantum Chemistry by Ira N. Levine, Chap. 13, Sec. MO theory of H2+):

  Overlap integral    Sab = (1 + k*R + k*k*R*R/3) * exp((-1)*k*R)
  Coulomb integral    Haa = 0.5*k*k - k - 1/R + (k+1/R) * exp((-2)*k*R)
  Resonance Integral  Hab = (-0.5)*k*k*Sab - k*(2-k)*(1+k*R)*exp((-1)*k*R)
  Internuclear Potn.  U   = (Haa + Hab)/(1 + Sab) + 1/R
  (Electronic energy)


  Value of the orbital exponent k for each value of R is obtained as the
  optimum value that gives the lowest value of U (variation theorem).

 Internuclear   Orbital      Overlap     Coulomb    Resonance  Electronic
  Distance R   Exponent k   Integral    Integral    Integral    Energy U
 (AtomicUnit) (PureNumber)  Sab(a.u.)   Haa(a.u.)   Hab(a.u.)    (a. u.)

    0.40000     1.83270
    0.60000     1.72620
    0.80000     1.62690
    1.00000     1.53790
    1.20000     1.45980
    1.40000     1.39190
    1.60000     1.33310
    1.80000     1.28250
    2.00000     1.23870
    2.20000     1.20090
    2.40000     1.16830
    2.60000     1.14010
    2.80000     1.11580
    3.00000     1.09490
    3.20000     1.07690
    3.40000     1.06160
    3.60000     1.04860
    3.80000     1.03750
    4.00000     1.02830
    5.00000     1.00200
    6.00000     1.00000
    7.00000     1.00000
    8.00000     1.00000