Page 56 - 71 the abc of dft_opt
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13.5. QUESTIONS 111 112 CHAPTER 13. ADIABATIC CONNECTION
must chose if we wish to break spin-symmetry or not. If we allow symmetry breaking, we will
get the λ = 1 end about right, but have a flat curve, and so overestimate the magnitude of
the correlation energy. On the other hand, if we don’t, we will get a curve that bends just a
little down from the λ = 0 end, and so underestimate the correlation.
As we will see throughout the rest of this book, this is a very important problem for DFT
in quantum chemistry. Many molecules exhibit similar behavior, not in their total energies,
but in their energy differences between bonded and dissociated states.
Exercise 66 Adiabatic connection for stretched H 2
Draw an accurate adiabatic connection curve for H 2 with a bond length of 20 ˚ A.
13.5 Questions
1. Using the high-density limit of Wigner correlation, estimate roughly how large the corre-
lation energy usually is within LDA.
