Atomic and molecular orbitals ( e . . ( 2 p , or the HOMO of benzene ) are described by linear combinations of basis functions ( 4 3 4 = Lapi In

i understand that it is a bunch of questions about scalar products so i would integrate. I'm just not entirely sure on the math because of the basis set

Atomic and molecular orbitals ( e . . ( 2 p , or the HOMO of benzene ) are described by linearcombinations of basis functions ( 4 34 = LapiIn computational chemistry , a simple basis set for the radial wavefunction ( we ignore the angularpart here ) is given by Slater - Type Orbitals , or STOsRn ( r ) = Non - 1 e - 35Note that it is customary to use the notation Ry rather than ; for this purpose . Each function Innormalized by a constant , N , ? gives the spatial extent of the orbital determined by the nuclearcharge , is the distance between nucleus and electron , and n is related to the orbital number ( e . gin2 in a hydrogen 2 p orbital ) . Recall that an orbital , Rn , describes a probability density for thelocation of an electron . Let's consider a small STO basis set consisting of n = 1 2 3 4 , and no otherfunctions on the domain Or < coa ) What is the norm , ( RA RA ) , necessarily ? ( Do not do a calculation . )b ) Is N the same or different for each basis function ? If not , find a general form for N. HintSo Deb e - axe doc( ) Calculate ( Ra RA ) . Are these functions orthogonal ? By analogy to this exercise , is the basis seorthogonal in general1 ) Write the formal expression for the expansion in the STO basis of an arbitrary function of ( ) . Iff ( ) were expanded in an orthonormal basis set , how would you calculate its coefficients , on ?e ) If you determined in ( c ) that the STO basis set is not orthogonal , how does the determination ofcoefficients , On , change ?