TDDFT in Chemistry and Biochemistry III - TDDFT.org

More documents

Recommendations

Info

Linear ResponseOperator notationDefine operators Λ and ∆ on L,( ) A BΛ = ; ∆ =B ALinear response equation takes the form( ) 1 00 −1(Λ − ω∆)|X , Y 〉 = −|P, Q〉Frequency-dependent polarizability α mn (ω)External perturbation is external electric field (dipole approximation)|P n , Q n 〉 = |µ n , µ n 〉 ; α mn (ω) = 〈µ m , µ m |X ω,n , Y ω,n 〉∫µ m ia = d 3 r ϕ i (r, σ) r m ϕ a (r, σ) , m, n ∈ {x, y, z}Dmitrij Rappoport (Harvard U.) TDDFT in Chemistry III TDDFT Winter School 2010 12 / 22
Linear ResponseFrequency-dependent polarizability α(ω) of fullerene C 60680650α, a.u.630610590570550300 500 700 9001100Wavelength, nmPolarizability α(ω) of C 60 diverges at λ = 350 nm (3.54 eV)PBE0/SVPs basis setDmitrij Rappoport (Harvard U.) TDDFT in Chemistry III TDDFT Winter School 2010 13 / 22
Page 1 and 2: TDDFT in Chemistry and Biochemistry
Page 3 and 4: All Roads Lead to RomeFrequency-Dom
Page 5 and 6: Kohn-Sham Orbital ResponseGround st
Page 7 and 8: Density Matrix FormulationDensity m
Page 9 and 10: Density Matrix FormulationCoupling
Page 11: Linear ResponseEquation of motion f
Page 15 and 16: Higher-Order ResponseFrequency-depe
Page 17 and 18: Strategies for Solving Matrix Equat
Page 19 and 20: Strategies for Solving Matrix Equat
Page 21 and 22: Electronic Polarizabilities of Mole

TDDFT in Chemistry and Biochemistry III - TDDFT.org

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?