1. Calculate the correlation energy for He using the results in the table above

Question

1. Calculate the correlation energy for He using the results in the table above in eV

2. Calculate the ratio of the correlation energy to the total energy for He using the results in the table above.

Problem 21.12 The exact energy of a ground state He atom is -79.01 ev. Total energy and 1s orbital energy for He for three different basis sets used to represent the 1s orbital are shown in the table. Total Energy 18 Orbital Number of Etotal 2E1. Exponents, Basis G He, Etotal (e ergy, E18 (evo (e Functions, m 1.41714, 2.37682, -24.9787 4.39628, 6.52699, -77.8703 -27.9129 7.94252 -24.9787 2.91093, 1.45363 -77.8701 -27.9133 -28.6998 1.68750 -77.4887 -24.3945

Explanation / Answer

Ans;- 1

From the table given (For the first set)

Hartree Fock energy = - 27.9129eV

Total Energy = - 77.8703

Correlation energy = Total energy - hartree fock energy

                             = - 77.8703 + 27.9129

                            = - 49.95eV

Ans 2 . Ratio = - 49.95 / - 77.87

                    = 0.64

For set 2

Hartree- Fock energy = -27.9133

total energy= -77.8701

Correlation energy = -77.8701+27.9133

                            = -49.95eV

Ratio= -0.64

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