Transcript NMR spin spin couplings for heavy elements

Density Functional
Implementation of the
Computation of Chiroptical
Molecular Properties
With Applications to the
Computation of CD Spectra
Jochen Autschbach & Tom Ziegler,
University of Calgary, Dept. of Chemistry
University Drive 2500, Calgary, Canada, T2N-1N4
Email: [email protected]
1
Motivation

Almost all biochemically relevant substances
are optically active
 CD (circular dichroism) and ORD (optical
rotation dispersion) spectroscopy are
important methods in experimental research
 Interpretation of spectra can be difficult,
overlapping CD bands obscure the spectra …
Prediction of chiroptical properties by firstprinciples quantum chemical methods will be an
important tool to asssist chemical and
biochemical research and enhance our understanding of optical activity
2
Methodology
Quantifying Optical Activity
Light-Wave interacts with
a chiral molecule

O

electric dipole moment in a
time-dependent magnetic
field (B of light wave)
perturbed
electric &
magnetic
moments
'  
 B
c t

or m
CH3
magnetic dipole moment in a
time-dependent electric field
(E of light wave)
; m'  
 E
c t
 is the
optical
rotation
parameter
3
Methodology
Sum-Over-States formalism yields
2c
R 0
  2
2
3   0  
frequency dependent
optical rotation parameter 
ORD spectra
Excitation Frequencies 0
Rotatory Strengths R0
R 0  Im(0   m0 )
electric
magnetic
Related to transition transition
the CD
dipole
dipole
spectrum

R0   const.   dE 
E
CD Band
4
Methodology
Direct computation of  and R with TDDFT
Frequency dependent electron density change (after FT)
' ( )    Pia ( ) i
i
*
a
 = molecular orbitals,
occupation # 0 or 1
a
Pia ()  Pai* ()
Fourier-transformed density matrix
due to the perturbation (E(t) or B(t))
oc c vi rt
X ai  Pai
Yai  Pia
' ( )    (X ai  Yai ) (er )ai
i
a
oc c vi rt
e
m' ( )    (Xai  Yai ) ( r  pˆ ) ai
2c
i
a
5
Methodology
Direct computation of  and R with TDDFT
RPA-type equation system for P, iocc, a virt
A
B
1
0
X
V

















B A  0 1
Y W
Wai  Via
X = vector containing
all (ai) elements, etc…
matrix elements of the external perturbation,
(-dependent Hamiltonian due to E(t) or B(t))
A,B are matrices. They contain of the response of the system
due to the perturbation (first-order Coulomb and XC potential)
We use the ALDA Kernel (first-order VWN potential) for XC
6
Methodology
Direct computation of  and R with TDDFT
1
Definitions: S  (A  B)

F  F
[   ]   2
2
   
2
2 1
1 / 2
;   S (A  B)S
1/ 2
The F’s are the eigenvectors of
, 2 its eigenvalues (=
excitation frequencies)
Skipping a few lines of straightforward algebra,we obtain
1/ 2
  2 Im(DS
1
1/ 2
[   ] S
M)
Dai  (er )ai dipole moment matrix element s
e
Mai  ( r  pˆ ) magnet ic moment matrix elements
2c
7
Methodology
Direct computation of  and R with TDDFT
Comparison with the Sum-Over-States Formula yields for R0
1 / 2
R0   Im( DS
 1/ 2
F  F S
M)
Therefore
0  
1 / 2
1 / 2
DS
1/ 2
m0    MS
3 /2
F
F
consistent with definition of oscillator strength in TDDFT,
obtained as
2
f 0 
1/ 2
3
| DS
2
F |
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Implementation into ADF





Excitation energies and oscillator strengths already available in the Amsterdam Density
Functional Code (ADF, see www.scm.com)
Only Mai matrix elements additionally needed for
Rotatory Strengths (, D, S, F already available)
Computation of Mai by numerical integration
Abelian chiral symmetry groups currently supported for computation of CD spectra (C1, C2, D2)
Implementation for  in progress (follows the
available implementation for frequency dependent
polarizabilities
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Implementation into ADF





Additionally, the velocity representations for the
rotatory and oscillator strengths have been
implemented (matrix elements ai)
Velocity form of R is origin-independent
Differences between R and R typically ~ 15% for
moderate accuracy settings in the computations
Computationally efficient, reasonable accuracy for
many applications
Suitable Slater basis sets with diffuse functions
need to be developed for routine applications
10
Applications
H
(R)-Methyloxirane
Excit.
1
E/eV
f
R/1040cgs
2-4
<E>/eV
Sf
SR/1040cg
s
H
O
H
CH3
ADF
ADF
Other
Other
Expt.
GGA a)
SAOP b)
Ref [1]
Ref [2]
Ref [2]
6.05
0.011
7.11
0.013
6.0
0.012
6.4
7.12
0.0004 0.025
-10.2
6.59
-13.4
7.69
-23.0
6.5
-2.66
7.3
0.047
+9.75
0.061
+14.7
0.044
+23.0
0.0012 0.062
+2.24 11.8
[1] TD LDA: Yabana & Bertsch, PRA 60 (1999), 1271
[2] MR-CI: Carnell et al., CPL 180 (1991), 477
a) BP86 triple-zeta + diff. Slater basis b) SAOP potential
-11.8
7.75
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Applications
H
(S,S)-Dimethyloxirane
ADF CD Spectra simulation *)
O
H3C
CH3
H
Exp. spectrum / MR-CI simulation [1]
Rcalc = 7.6
Rexp. = 9.5
calc. predicts large neg.
R for this excitation
low
lying Rydberg excitations, sensitive to
basis set size / functional
good agreement with exp. and MR-CI study
for R of the 1st excitation
E for GGA ~ 1eV too small, but well
reproduced with SAOP potential
[1] Carnell et al., CPL 179 (1994), 385
*) Assumed linewidth proportional to E (approx. 0.15 eV), Gaussians centered at
excitation energies reproducing R , ADF Basis “Vdiff” (triple-z + pol. + diff)
12
Applications
H14
O
Cyclohexanone Derivatives
H7
C=O ~290 nm (4.4 eV) pp* transition
H?  CH3 a)
Ecalc/eV
H13
H10
H11
H8
H9
Rcalc
R Other
R Other
R Expt.
GGA b)
Ref [1]
Ref [2]
Ref [1] c)
none
H7
3.94 (4.3) b) 0
0
0
0
3.96 (4.3)
0.27
0.00
9.92
+(small)
H9
3.96 (4.3)
-1.39
-2.26
-15.11
- d)
H7H13
3.96 (4.3)
+1.46
+3.6
+5.53
+1.7
H7H13H8
3.99 (4.3)
+4.36
+5.3
+6.36
+6.2
H12
[1] CNDO: Pao & Santry, JACS 88 (1966), 4157. [2] Extended Hückel: Hoffmann & Gould,
JACS 92 (1970), 1813.
a) Numbered hydrogens substituted with methyl groups. Same geometries used than in
[1],[2] b) BP86, triple-zeta Slater basis,
numbers in parentheses: SAOP functional, SAOP R’s almost identical
c) As quoted in [1]. Exp. values are computed from ORD spectra d) magnitude not known
13
Applications
Hexahelicene
ADF CD Spectra simulation *)
Exp. / theor. study [1]
SRtheo = 412
SRexp = 331
Shape
of the spectrum equivalent to the
TDDFT and exp. spectra published in [1]
magnitude of R‘s smaller than exp., in
particular for the short-wavelength excitations
(TDDFT in [1] has too large R ‘s for the “B”
band, too small for “E” band)
GGA / SAOP yield qualitatively similar results
*)
preliminary Results with ADF Basis IV (no diff.) [1] TDDFT/Expt. Furche et al., JACS 122 (2000), 1717
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Applications
Chloro-methyl-aziridines
ADF simulation *)
Exp. Spectra [1]
CH3
2
N
CH3
Cl
CH3
N
Cl
1b
CH3
Cl
N
1a
GGA, shifted +0.7 eV
SAOP
yields comparable E than
GGA
Exp. spectra qualitatively well reproduced, for 1a,1b
magni tudes for 
also comparable
to experiment
(+)Band at ~260 nm
for 2 much stronger
in the simulations
(low experimental
resolution ?)
Blue shift for 1b is
not reproduced
[1] in heptane, Shustov et al., JACS 110 (1988), 1719.
*)
BP86 functional, ADF Basis “Vdiff” Triple-z +pol. + diff. basis
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Summary and Outlook

Rotatory strengths are very sensitive to basis set size
and the chosen density functional
 GGA excitation energies are systematically too low.
The SAOP potential is quite accurate for small
hydrocarbon molecules with large basis sets, but not
so accurate for 3rd row elements. Standard GGAs
yield comparable results for these elements.
 Qualitative features of the experimental CD spectra
are well reproduced in particular for low lying
excitations.
 Solvent effects can be important in order to achieve
realistic simulations of CD spectra. Currently, solvent
effects are neglected.
 Implementation for ORD spectra in progress
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