The hydrogen molecular ion wavefunctions

Upon obtaining the energies of the molecular orbitals by solving the secular determinant [eq. (3.1.17)], we are now ready to proceed to determine the coefficients ci and C2 of eq. (3.1.16). To do this we need to solve the secular equations 

Wavefunction xjrs is called a bonding orbital, as its energy is lower than that of its constituent atomic orbitals (c.f. Fig. 3.1.3). 

Now we examine the bonding orbital tis and antibonding orbital ax as well as their probability density functions tis 2 and ct s 2. A schematic representation of cr is is shown in Fig. 3.1.5(a). In this combination of two Is orbitals, electron density accumulates in the internuclear region. Also, crls has cylindrical symmetry around the internuclear axis. 

Probability density distribution of Hj plotted along the internuclear axis  

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