A two-center correlated orbital approach was used to calculate the electronic ground state energy for the HeH+ molecular ion. The wavefunctions were constructed from the exact solution of the Schrdinger equation for the HeH++ problem in prolate-spheroidal coordinates taken together with a Hylleraas type correlation factor. With a simple single term wavefunction,we obtained ground state energy of -2.95308691 hartree without any variational parameters in the calculation. When a two-configuration-state wavefunction was used and effective charges were allowed to be adjusted,we found an energy of -2.97384868 hartree,which is to be compared with -2.97869074 hartree obtained by an 83 term configuration interaction wavefunction or -2.97364338 hartree by an ab initio calculation (at the MP4(SDQ)/6-311++G(3df,3dp) level) using the well-known “canned” code. A two-center correlated orbital approach was used to calculate the electronic ground state energy for the HeH + molecular ion. The wavefunctions were constructed from the exact solution of the Schrödinger equation for the HeH ++ problem in prolate-spheroidal coordinates taken together with a Hylleraas type correlation factor. With a simple single term wavefunction, we obtained ground state energy of -2.95308691 hartree without any variational parameters in the calculation. When a two-configuration-state wavefunction was used and effective charges were allowed to be adjusted, we found an energy of -2.97384868 hartree, which is to be compared with -2.97869074 hartree obtained by an 83 term configuration interaction wavefunction or -2.97364338 hartree by an ab initio calculation (at the MP4 (SDQ) / 6-311 ++ G (3df, 3dp ) level) using the well-known “canned ” code.