Quantum Chemistry / Quantum Mechanics Perturbation Theory
Electric field in an atom much larger than fields in a laboratory
Basic idea H = H0 + V small as operators: small constant
known problem, e.g. HF of a molecule because V is small, we hope that Taylor expansions quickly converge
Solution – polynomial comparison
Solution – polynomial comparison
known problem, e.g. HF of a molecule “PT2”
example: HF H = HHF + V, V = H - HHF = 0 Møller-Plesset, “MP2” “MP3” MP4, MP6, MP12 ... .. most frequent, ~ N5
Example - HO
Wavefunction ... note: non-degenerate states only
Degenerate states Energie E1(0)= E2(0)=E3(0) H0 1(0) 2(0) 3(0) H0+V
... a general picture perturbations can have no effect, mix and split energy levels ...
Going beyond HF configuration interaction, CI PT: MP2, MP3, MP4 ... Monte Carlo, special methods Density functional theory
CI FCI = SE
CI FCI = SE
FCI ~ eN scaling limited CI – CIS, CISD, ... size – inconsistent E12 <> E1 + e2
Couple clusters Jiří Čížek
Coupled Cluster – Most Used Approximations CCSD, CCSDT, CCSDT(Q), “golden standard” “chemical accuracy”, 0.1 kcal/mol
CC – kind of complicated, for example
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