Quantum Chemistry Quantum Mechanics Perturbation Theory Electric field

Quantum Chemistry / Quantum Mechanics Perturbation Theory

Electric field in an atom -much larger than fields in a laboratory

Basic idea • H = H 0 + 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 “PT 2”

example: HF H = HHF + V, V = H - HHF =0 Møller-Plesset, “MP 2” “MP 3” MP 4, MP 6, MP 12. . . most frequent, ~ N 5

Example - HO

Wavefunction . . . note: non-degenerate states only

Degenerate states Energie H 0+V H 0 E 1(0)= E 2(0)=E 3(0) 1(0) 2(0) 3(0)

. . . a general picture perturbations can have no effect, mix and split energy levels. . .

Going beyond HF -configuration interaction, CI -PT: MP 2, MP 3, MP 4. . . -Monte Carlo, special methods -Density functional theory

CI FCI = SE

CI FCI = SE

FCI ~ e. N scaling • limited CI – CIS, CISD, . . . • size – inconsistent • E 12 <> E 1 + e 2

Couple clusters • Jiří Čížek

Coupled Cluster – Most Used Approximations CCSD, CCSDT(Q), “golden standard” “chemical accuracy”, 0. 1 kcal/mol

CC – kind of complicated, for example

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