Our Experience with TD-DFT and TD-DFTB in Biological, Bio-inspired, - PowerPoint PPT Presentation

Our Experience with TD-DFT and TD-DFTB in Biological, Bio-inspired, and Other Photoprocesses マーク , 卡西达 マーグ Mark E. Casida ( 樫田 マーグ 马克 ) Professeur, chimie théorique Laboratoire de Spectrométrie, Interactions et Chimie Théorique (SITh) Département de Chimie Moléculaire (DCM, UMR CNRS/UGA 5250) Institut de Chimie Moléculaire de Grenoble (ICMG, FR-2607) Université Grenoble Alpes (UGA) 301 rue de la Chimie CS 40700 38058 Grenoble cedex 9 France e-mail: mark.casida@univ-grenoble-alpes.fr SISSA Zoom Workshop Hosted by ICTP, Trieste, Italy 30 minutes CECAM SISSA ICTP 22/09-2020 1

Lester Earl CASIDA 1904–1986 Prof. Univ. Wisconsin, Madison American Society of Animal Science has named a scholarship for doctoral students in Reproductive Physiology in his honor. John Edward CASIDA 1929-2018 Lester Earl CASIDA Jr. Prof. Univ. Calif., Berkeley 1928-2017 Prof. Penn. State Univ. Entomology and toxicology Very distinguished (member USA Industrial and soil microbiology NAS, UK Royal Society, Wolf Discovered bacterium: Prize in Agriculture, ...) Ensifer adherens Casida 1982 Mark Earl CASIDA 1957-? Prof. Univ. Grenoble Alpes Theoretical Chemistry Casida equations for TD-DFT CECAM SISSA ICTP 22/09-2020 2

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OUTLINE I. PHOTOCHEMICAL THINKING II. ELECTRONIC EXCITED-STATE PROCESSES III. TD-DFT(B) IV. STATIC APPLICATIONS A. Luminescence indices B. Retinal C. Excitonic effects V. TD-DFT(B) FSSH VI. DYNAMICS APPLICATIONS A. Easy case: oxirane B. Hard case: pentacene/buckyball VII. CONCLUSION CECAM SISSA ICTP 22/09-2020 4

O X I R A N E P H O T O C H E MI S T R Y ). T . I b u k i , M. I n a s a k i e t Y . T a k e s a k i , J . C h e m . P h y s . 5 9 , 2 0 7 6 ( 1 9 7 3 CECAM SISSA ICTP 22/09-2020 5

LEWIS STRUCTURES Gomer-Noyes Mechanism [E. Gomer et W.A. Noyes, Jr., J. Am. Chem. Soc. 72, 101 (1950); T. Ibuki, M. Inasaki et Y. Takesaki, J. Chem. Phys. 59, 2076 (1973). ] CECAM SISSA ICTP 22/09-2020 6

ORBITAL THINKING: WOODWARD-HOFFMANN RULES CECAM SISSA ICTP 22/09-2020 7

S T A T E S : T WO - O R B I T A L T WO - E L E C T R O N MO D E L ( T O T E M) a a  i  a ∣ a i ∣  i i   a ∣ i a ∣ i   a i a a  i  i a   a ∣ a i ∣ ∣ i i ∣ ∣ i a ∣  i   i    S , M S Singlet = 1  a ∣ f H ∣ i  −  a ∣ f H ∣ i   ∣ a ∣    S = a − i  2 i a a i  0 ∣∣ i i a  , 0  2 Triplets  1 =∣ i ∣ a , 0 −  a ∣ f H ∣ i  = 1  T = a − i a i  ∣ a ∣    1 i ∣−∣ i a  , 0  2   1 =∣ ∣ a i , − 1 CECAM SISSA ICTP 22/09-2020 8

POTENTIAL ENERGY SURFACES (PESs) PRODUCT REACTANT PRODUCT Original image: J. Michl and V. Bonacic-Koutecky, Electronic Aspects of Organic Photochemistry (Wiley: New York, 1990), p. 71. Embellishment: E. Tapvicza. CECAM SISSA ICTP 22/09-2020 9

WAYS WE TRY TO UNDERSTAND PHOTOCHEMICAL MECHANISMS Lewis structures Orbital models Potential energy surfaces* Pathway approach Minimum energy pathways Funnels Dynamics Ehrenfest Surface hopping (Star Trek 3D chess) * J. Michl and V. Bonacic-Koutecky, Electronic Aspects of Organic Photochemistry (Wiley: New York, 1990) CECAM SISSA ICTP 22/09-2020 10

OUTLINE I. PHOTOCHEMICAL THINKING II. ELECTRONIC EXCITED-STATE PROCESSES III. TD-DFT(B) IV. STATIC APPLICATIONS A. Luminescence indices B. Retinal C. Excitonic effects V. TD-DFT(B) FSSH VI. DYNAMICS APPLICATIONS A. Easy case: oxirane B. Hard case: pentacene/buckyball VII. CONCLUSION CECAM SISSA ICTP 22/09-2020 11

SOME EXAMPLES OF EXCITED-STATE PROCESSES IN BIOLOGY (all fall under a generalized notion of “photochemistry”) CECAM SISSA ICTP 22/09-2020 12

PHOTOPHYSICS: * → A A + h ν → A Radiationless relaxation Luminescence Fluoresence Phosphorescence Example: green fluorescent protein http://zeiss-campus.magnet.fsu.edu/print/probes/fpintroduction-print.html CECAM SISSA ICTP 22/09-2020 13

PHOTOCHEMISTRY * → B + C A + h ν → A Example: vision (rhodopsin) https://www.ncbi.nlm.nih.gov/books/NBK52768/ CECAM SISSA ICTP 22/09-2020 14

CHEMILUMINESCENCE * → A + h ν B + C → A Example: firefly luciferon CECAM SISSA ICTP 22/09-2020 15

* → B + C A + h ν → A * → B + C A +Δ→ A E.H. White, J. Wiecko, and D.F. Roswell, “Photochemistry without light”, J. Am. Chem. Soc. 91 , 5194 (1969). CECAM SISSA ICTP 22/09-2020 16

* + B → A + B * A EXCITONS + + B - → A - + B + A Example: photosynthesis Excitons may be: Real --- energy and charge transfer Fictitious --- needed to understand complex systems From a presentation by Neil Greenham https://www.slideshare.net/cdtpv/thursday-42325335 CECAM SISSA ICTP 22/09-2020 17

OUTLINE I. PHOTOCHEMICAL THINKING II. ELECTRONIC EXCITED-STATE PROCESSES III. TD-DFT(B) IV. STATIC APPLICATIONS A. Luminescence indices B. Retinal C. Excitonic effects V. TD-DFT(B) FSSH VI. DYNAMICS APPLICATIONS A. Easy case: oxirane B. Hard case: pentacene/buckyball VII. CONCLUSION CECAM SISSA ICTP 22/09-2020 18

Cartoon given to me 1995 by Jean-Paul Malrieu CECAM SISSA ICTP 22/09-2020 19

Presentation uploaded by Deddy Tedjo https://slideplayer.com/slide/17033333/ CECAM SISSA ICTP 22/09-2020 20

T I ME - D E P E N D E N T D E N S I T Y - F U N C T I O N A L T H E O R Y ( T D D F T ) [ E . R u n g e a n d E . K . U . G r o s s , P h y s . R e v . L e t t . 5 2 , 9 9 7 ( 1 9 8 4 ) ] F o r a s y s t e m , i n t i a l l y i n i t s g r o u n d s t a t e , e x p o s e d t o t i m e - d e p e n d e n t p e r t u r b a t i o n : R u n g e - G r o s s T h e o r e m : v ( r t ) i s d e t e r m i n e d b y  ( r t ) u p t o a n a d d i t i v e e x t f u n c t i o n o f t i m e t C  t '  dt ' C o r o l l a r y : − i ∫ t 0 rt  N ,v ext  r t  C  t   H  t  C  t   t  e  ( R G 1 a s s u m e s f u n c t i o n s w i t h T a y l o r s e r i e s . ) CECAM SISSA ICTP 22/09-2020 21

TIME-DEPENDENT KOHN-SHAM EQUATION [E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52 , 997 (1984)] [ − 1  ]  i  ∫  r ' t  ∂ 2 (1) ∇  v  r t d r '  v  r t  r t = i  i  r t   e x t x c 2 ∣ r − r ' ∣ ∂ t 2 = ∑ i where  r t  n  ∣ i   r t ∣ (2) i  A [] and x c (3)  = v r t x c    r t CECAM SISSA ICTP 22/09-2020 22

E l e c t r i c - F i e l d I n d u c e d E l e c t r o n i c P o l a r i z a t i o n photon O  t   H H H H H H H H ℏ 0 Classical model of a photon   t =  cos  0 t  v  r t = e    t  r ⋅ Induced dipole moment  t =− e  0 ∣ r ∣ 0  t  0  t ∣ r ∣ 0    CECAM SISSA ICTP 22/09-2020 23

THE DYNAMIC POLARIZABILITY  i  t = i  ∑ j  i , j  j cos  t ⋯ 2  I  0 ∣ r i ∣ I  I ∣ r j ∣ 0  f  r i ,r j = ∑ I ≠ 0 I 2 − 2  I Sum-over-states (SOS) theorem f I = ∑ I ≠ 0  I 2 − 2  I f I = 2 2 ∣ 0 ∣ y ∣ I ∣ 2 ∣ 0 ∣ z ∣ I ∣ 2   I ∣ 0 ∣ x ∣ I ∣ 3 How to make computationally convenient? CECAM SISSA ICTP 22/09-2020 24

COMPUTATIONALLY CONVENIENT FORMULATION Ma r k E . C a s i d a i n R e c e n t A d v a n c e s i n D e n s i t y F u n c t i o n a l Me t h o d s , P a r t I , e d i t e d b y D . P . C h o n g ( S i n g a p o r e , Wo r l d S c i e n t i fi c , 1 9 9 5 ) , p . 1 5 5 . " T i m e - d e p e n d e n t d e n s i t y - f u n c t i o n a l r e s p o n s e t h e o r y f o r m o l e c u l e s ' ' “RPA” equation  ]  I  = I ]  I    [ X [ X A  I  B  I  1 0 (1) I I   0 − 1 B  I  A  I Y Y where A  =  ,   i  j  j  − j   K   (2) i j  , k l , k , l i j  , k l B  = K   (3)  ,  , i j k l i j l k Coupling matrix  ,    = ∫∫ ∗ i (4) K   r  j   r  f r , r ' ;  k   r ' ∗ l   r '  d r d r '    i j  , k l H x c CECAM SISSA ICTP 22/09-2020 25