Concise Physical Chemistry

c17 JWBS043-Rogers September 13, 2010 11:28 Printer Name: Yet to Come

286 THE VARIATIONAL METHOD: ATOMS

normalization constant, equal to the wave function of He. Expand the determinant.

What is the normalization constant?

Problem 17.8

We have seen that the linear combination that is thedifferencebetween terms is

equivalent to theSlater determinantalwave function for helium.

ψHe(1,2)=

1

√

n

( 1 s(1)α(1)1s(2)β(2)− 1 s(2)α(2)1s(1)β(1))

≡

1

√

n

∣

∣

∣

∣

∣

1 s(1)α(1) 1 s(1)β(1)

1 s(2)α(2) 1 s(2)β(2)

∣

∣

∣

∣

∣

What is wrong with the positive combination?

ψHe(1,2)

1

√

n

( 1 s(1)α(1)1s(2)β(2)+ 1 s(2)α(2)1s(1)β(1))

Hint: Try switching electronsψHe(1,2)→ψHe(2,1).

Problem 17.9

A variational treatment of atomic helium gave

EHe=−(− 2 Z^2 eff+

5

4

Zeff+ 4 Zeff(Zeff−2))EH

FindZeffandEHegiven thatEH=− 13 .6 eV. Give your answer also in electron volts.

The experimental result isEHe=− 79 .0 eV. What is the % error of this variational

treatment?