Plenary lecture of the XVIII B-MRS Meeting given by Prof. Stefano Baroni (SISSA, Italy) on September 23, 2019 at Balneário Camboriú (Brazil).

1. Stefano Baroni
Scuola Internazionale Superiore di Studi Avanzati
Trieste — Italy
watching flowers through a silicon glass
multiscale simulation of the color optical properties of natural dyes
keynote talk given at the XVIII meeting of the Brazilian Materials Research Society, Balneário Camboriú, September 22-26, 2019

2. natural dyes in the food industry

3. natural dyes in the food industry
☛ global market of 1.45 billion USD in 2009
☛ total production of 50,000 tons / year
alcohols
5%
soft drinks
28%
food
67%
Other
18%
China
8%
Japan
10%
USA
28%
Europe
36%
☛ natural dyes market grown by 35% in the 2005-2009 quinquennium

4. the food industry is subject to an
increasing global pressure from
customers and lawmakers who
demand a shift towards ingredients
and additives that are perceived as
more natural and, “therefore”, healthier

5. the Southampton six
In 2007 Research funded by the UK FSA was
published, suggesting that the consumption of
certain mixes of artificial food colours and
preservatives could be linked to attention
deficit and increased hyperactivity in some
children.
Fact Sheet
Box A: The Seven
Southampton Additives
Colours:
Tartrazine (E102)
Quinoline yellow (E104)
Sunset yellow (E110)
Carmoisine (E122)
Ponceau 4R (E124)
Allura red (E129)
Preservative:
Sodium benzoate (E211)
Food additives are chemicals which are found
in the majority of ‘processed’ foods and drinks
consumed in the UK and abroad. They can
be from natural sources or artificially
manufactured. They are used to make food
look and taste more appealing, to maintain
consistency between batches and help
increase the ‘shelf life’ by preventing the food
from going mouldy or stale.
By law, if any additive is present in a product,
it must be listed on the ingredients list on the
packaging of food or drink bought in shops.
Additives can be listed either by name or by
their ‘E number.’ If you buy food at a
restaurant or take away outlet or a bakery you
may not know which additives are present as
the foods are not required to have ingredients
lists.
The chemicals in question are allowed to be
added, but some people say we do not know
enough about all of the health effects that
might be caused by these chemicals. For
instance Tartrazine (E102), has long been
known to cause rashes/skin irritation in a
small number of people, and others such as
Sodium Benzoate (E211) have been linked to
the worsening of asthma conditions. Some
additives that are permitted for use in the UK
and Europe are banned in other countries.
Recently, the UK Government body
responsible for food safety, the Food
Standards Agency (FSA), commissioned a
research project that became known as the
‘Southampton study.’ The Southampton study
demonstrated that mixtures of the seven
Since 2010 an EU-wide compulsory
warning must be put on any food
and drink product that contains any
of these six colours:
“May have an adverse
effect on activity and
attention in children”

6. natural dyes: the requirements

7. natural dyes: the requirements
tunable

8. natural dyes: the requirements
tunable
stable

9. natural dyes: the requirements
tunable
stable
safe

10. natural dyes: the requirements
tunable
stable
safe
inexpensive

11. carotenoids&cur
cuminoids
chlorofylls
flavonoids

12. carotenoids&cur
cuminoids
chlorofylls
flavonoids
anthocyanins

13. anthocyanins

14. anthocyanins
B
chromenylium
O
R5
O O
HO
HO
OH
OH
1
2
3
45
6
R7
R3'
R4'
R5'7
8 1'
2'
3'
4'
5'
6'

15. anthocyanins
anthocyanin R3’ R4’ R5’ R7
cyanin −OH −OH −H −OH
B
chromenylium
O
R5
O O
HO
HO
OH
OH
1
2
3
45
6
R7
R3'
R4'
R5'7
8 1'
2'
3'
4'
5'
6'

16. anthocyanin R3’ R4’ R5’ R7
cyanin −OH −OH −H −OH
peonin −OCH3 −OH −H −OH
anthocyanins
B
chromenylium
O
R5
O O
HO
HO
OH
OH
1
2
3
45
6
R7
R3'
R4'
R5'7
8 1'
2'
3'
4'
5'
6'

17. anthocyanin R3’ R4’ R5’ R7
cyanin −OH −OH −H −OH
peonin −OCH3 −OH −H −OH
rosinin −OH −OH −H −OCH3
anthocyanins
B
chromenylium
O
R5
O O
HO
HO
OH
OH
1
2
3
45
6
R7
R3'
R4'
R5'7
8 1'
2'
3'
4'
5'
6'

18. anthocyanin R3’ R4’ R5’ R7
cyanin −OH −OH −H −OH
peonin −OCH3 −OH −H −OH
rosinin −OH −OH −H −OCH3
malvin −OCH3 −OH −OCH3 −OH
anthocyanins
B
chromenylium
O
R5
O O
HO
HO
OH
OH
1
2
3
45
6
R7
R3'
R4'
R5'7
8 1'
2'
3'
4'
5'
6'

19. anthocyanins
anthocyanin R3’ R4’ R5’ R7
cyanin −OH −OH −H −OH
peonin −OCH3 −OH −H −OH
rosinin −OH −OH −H −OCH3
malvin −OCH3 −OH −OCH3 −OH
pelargonin −H −OH −OH −OH
B
chromenylium
O
R5
O O
HO
HO
OH
OH
1
2
3
45
6
R7
R3'
R4'
R5'7
8 1'
2'
3'
4'
5'
6'

20. anthocyanin R3’ R4’ R5’ R7
cyanin −OH −OH −H −OH
peonin −OCH3 −OH −H −OH
rosinin −OH −OH −H −OCH3
malvin −OCH3 −OH −OCH3 −OH
pelargonin −H −OH −OH −OH
delphinin −OH −OH −OCH3 −OH
anthocyanins
B
chromenylium
O
R5
O O
HO
HO
OH
OH
1
2
3
45
6
R7
R3'
R4'
R5'7
8 1'
2'
3'
4'
5'
6'

21. very little is known of the
molecular mechanisms that
determine the chromatic
properties and the stability of
anthocyanins and the relation
between structure and color

22. what color is all about
?

23. what color is all about

24. what color is all about

25. what color is all about

26. what color is all about
anycolor(λ) = r(λ) + g(λ) + b(λ)
450 550 650
λ[nm]

27. what color is all about
stimulus =
illuminant × transmission × sensitivity

28. S(λ) × e−κ(λ)x
× rgb(λ)<latexit sha1_base64="tRWmyqedvyyoKrRi3CKD2xRQhwQ=">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</latexit>
stimulus =
illuminant × transmission × sensitivity
what color is all about
!
!"#
!
$"#
!
""#
!
%"#
!
&"#
'()*+,
-./01234(
560.7(589:47;+!"#$

29. S(λ) × e−κ(λ)x
× rgb(λ)<latexit sha1_base64="tRWmyqedvyyoKrRi3CKD2xRQhwQ=">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</latexit>
stimulus =
illuminant × transmission × sensitivity
what color is all about
!
!"#
!
$"#
!
""#
!
%"#
!
&"#
'()*+,
-./01234(
560.7(589:47;+!"#$
T(x, )
x
absorbing mediumlight

30. S(λ) × e−κ(λ)x
× rgb(λ)<latexit sha1_base64="tRWmyqedvyyoKrRi3CKD2xRQhwQ=">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</latexit>
stimulus =
illuminant × transmission × sensitivity
what color is all about
400 500 600 700
κ(λ)
λ[nm]
!
!"#
!
$"#
!
""#
!
%"#
!
&"#
'()*+,
-./01234(
560.7(589:47;+!"#$
S(λ) × e−κ(λ)x
× rgb(λ)<latexit sha1_base64="tRWmyqedvyyoKrRi3CKD2xRQhwQ=">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</latexit>

31. S(λ) × e−κ(λ)x
× rgb(λ)<latexit sha1_base64="tRWmyqedvyyoKrRi3CKD2xRQhwQ=">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</latexit>
stimulus =
illuminant × transmission × sensitivity
what color is all about
400 500 600 700
κ(λ)
λ[nm]
!
!"#
!
$"#
!
""#
!
%"#
!
&"#
'()*+,
-./01234(
560.7(589:47;+!"#$
b rg
rgb
λ[nm]
S(λ) × e−κ(λ)x
× rgb(λ)<latexit sha1_base64="tRWmyqedvyyoKrRi3CKD2xRQhwQ=">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</latexit>
S(λ) × e−κ(λ)x
× rgb(λ)<latexit sha1_base64="tRWmyqedvyyoKrRi3CKD2xRQhwQ=">AAACu3icbVHLbhMxFPUMrxJeaSuxgYXVCilIZTQJ6muBVMGGFSqCNJEyIfJ4biYmtmdke1Ajy9/CN/AL/AVbvgTPJIG05UrXujrX59xXWnKmTRz/CsJbt+/cvbd1v/Xg4aPHT9rbOxe6qBSFPi14oYYp0cCZhL5hhsOwVEBEymGQzt/V+cE3UJoV8rNZlDAWJJdsyigxHpq0f9qkERmpPB3bODo9PYij4/o57LlEEDNTAn/qJNxLZuSlayWGCdC4tcpZcF/sq2siRwcrd8mclCX5R79cC6zpiYFL05CtgsxZ5TaQXAFIZ/NNjC6Ih1Ln/opO2vt137E3fDPoRnFj+2d7KPz+9Mfz80n7d5IVtBIgDeVEa0uUYZSD763SUBI6JzmMfCiJ73Rsm8IOv/BIhqeF8i4NbtBNhiVC64VI/c96OH09V4P/y40qMz0ZWybLyoCky0LTimNT4PpkOGMKqOELHxCqmO8V0xlRhBp/2CtVqEgVy2fGtZqlLCfHN4P1Ui56Ufd11Pvot/MWLW0LPUN7qIO66BidoffoHPURDTrBh2AQDMM3IQ2/hnz5NQxWnF10xcLqDwVh3Rc=</latexit>

32. RGB(x) = S(λ)e−κ(λ)x
rgb(λ)dλ
<latexit sha1_base64="0MdJub8hIxVv1BEW5lJ72Clbakc=">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</latexit>
400 500 600 700
κ(λ)
λ[nm]
what color is all about
!
!"#
!
$"#
!
""#
!
%"#
!
&"#
'()*+,
-./01234(
560.7(589:47;+!"#$
b rg
rgb
λ[nm]
stimulus =
illuminant × transmission × sensitivity

33. how to predict the color optical
properties of materials?

34. The fundamental laws necessary for the
mathematical treatment of a large part of physics
and the whole of chemistry are thus completely known,
and the difficulty lies only in the fact that application of
these laws leads to equations that are too
complex to be solved.

35. The fundamental laws necessary for the
mathematical treatment of a large part of physics
and the whole of chemistry are thus completely known,
and the difficulty lies only in the fact that application of
these laws leads to equations that are too
complex to be solved.

36. The fundamental laws necessary for the
mathematical treatment of a large part of physics
and the whole of chemistry are thus completely known,
and the difficulty lies only in the fact that application of
these laws leads to equations that are too
complex to be solved.
xxx
were

37. vKS(r, t) = v (r) + E(t) x +
n(r , t)
|r r |
dr + vxc[n](r, t)
<latexit sha1_base64="pjmYTD7b28RCuG7Xzh2QlovYgYo=">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</latexit>
optical spectra from TDDF(p)T
E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)
i
⇥ v(r, t)
⇥t
= + vKS(r, t) v(r, t)
n(r, t) =
X
v
| v(r, t)|2

38. vKS(r, t) = v (r) + E(t) x +
n(r , t)
|r r |
dr + vxc[n](r, t)
<latexit sha1_base64="pjmYTD7b28RCuG7Xzh2QlovYgYo=">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</latexit>
optical spectra from TDDF(p)T
E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)
i
⇥ v(r, t)
⇥t
= + vKS(r, t) v(r, t)
(t) =
X
v
|⇥v(t)⇥ ⇥v(t)|
hA(t)i = Tr (t)A
n(r, t) =
X
v
| v(r, t)|2

39. vKS(r, t) = v (r) + E(t) x +
n(r , t)
|r r |
dr + vxc[n](r, t)
<latexit sha1_base64="pjmYTD7b28RCuG7Xzh2QlovYgYo=">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</latexit>
i ˙(t) =
⇥
HKS(t), (t)
⇤
optical spectra from TDDF(p)T
E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)
i
⇥ v(r, t)
⇥t
= + vKS(r, t) v(r, t)
(t) =
X
v
|⇥v(t)⇥ ⇥v(t)|
hA(t)i = Tr (t)A
n(r, t) =
X
v
| v(r, t)|2

40. optical spectra from TDDF(p)T
i ˙(t) =
⇥
HKS(t), (t)
⇤
⇢(t) = ⇢ + ⇢0
(t)
HKS(t) = H + E(t)x + V 0
HXC(t)<latexit sha1_base64="wsP3Pew6S0rkAwgxuivZVeMAVVg=">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</latexit>
i ˙⇢0
= [H ,⇢0
] + [V 0
HXC, ⇢ ] + E[x, ⇢ ] + O E2
<latexit sha1_base64="UrflNFMoCk4WXnGGxHhcghyqoYU=">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</latexit>

41. optical spectra from TDDF(p)T
i ˙(t) =
⇥
HKS(t), (t)
⇤
i ˙⇢0
= [H ,⇢0
] + [V 0
HXC(⇢0
), ⇢ ] + E[x, ⇢ ]<latexit sha1_base64="pTDA5FzwGtkMXqir3HJYg+oHIsk=">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</latexit>
⇢(t) = ⇢ + ⇢0
(t)
HKS(t) = H + E(t)x + V 0
HXC(t)<latexit sha1_base64="wsP3Pew6S0rkAwgxuivZVeMAVVg=">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</latexit>
i ˙⇢0
(t) = L ⇢0
(t) + E(t)[x, ⇢ ]<latexit sha1_base64="53gTiYannH8W8U2c3n6tV0dFjzM=">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</latexit>

42. (! L)˜⇢0
(!) = ˜E(!)[x, ⇢ ]<latexit sha1_base64="67B+IGz7ii9PUTaSy6tD4IB0is8=">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</latexit>
optical spectra from TDDF(p)T
i ˙(t) =
⇥
HKS(t), (t)
⇤
i ˙⇢0
= [H ,⇢0
] + [V 0
HXC(⇢0
), ⇢ ] + E[x, ⇢ ]<latexit sha1_base64="pTDA5FzwGtkMXqir3HJYg+oHIsk=">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</latexit>
⇢(t) = ⇢ + ⇢0
(t)
HKS(t) = H + E(t)x + V 0
HXC(t)<latexit sha1_base64="wsP3Pew6S0rkAwgxuivZVeMAVVg=">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</latexit>

43. (! L)˜⇢0
(!) = ˜E(!)[x, ⇢ ]<latexit sha1_base64="67B+IGz7ii9PUTaSy6tD4IB0is8=">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</latexit>
optical spectra from TDDF(p)T
TDDF(p)T: Lanczos’ recursion method
↵(!) = d, (! L) 1
· [x, ⇢ ]<latexit sha1_base64="MGGazuUEfvF59Cuu/aCOAA/rYbM=">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</latexit>

44. (! L)˜⇢0
(!) = ˜E(!)[x, ⇢ ]<latexit sha1_base64="67B+IGz7ii9PUTaSy6tD4IB0is8=">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</latexit>
optical spectra from TDDF(p)T
L ˜⇢0
= !˜⇢0 Casida’s equations: iterative
diagonalization of large
matrices (DIIS or Davidson)
D. Rocca et al. JCP 128, 154105 (2008)
X. Ge et al. Comp. Phys. Commun. 185, 2080 (2014)
TDDF(p)T: Lanczos’ recursion method
↵(!) = d, (! L) 1
· [x, ⇢ ]<latexit sha1_base64="MGGazuUEfvF59Cuu/aCOAA/rYbM=">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</latexit>

45. chlorophyll a
C55H72MgN4O

46. chlorophyll a
400 500 600 700
!
" [nm]
tddft (gga)
expt

47. chlorophyll a
400 500 600 700
!
" [nm]
tddft (gga)
expt

48. from chemistry to color
molecular
structure
chemical
composition

49. from chemistry to color
molecular
structure
chemical
composition
environmental
conditions
+

50. from chemistry to color
molecular
structure
chemical
composition
environmental
conditions
+
electronic
structure

51. from chemistry to color
molecular
structure
chemical
composition
environmental
conditions
+
absorption
spectrum
400 500 600 700
λ (nm)
electronic
structure

52. from chemistry to color
molecular
structure
chemical
composition
environmental
conditions
+
absorption
spectrum
400 500 600 700
λ (nm)
electronic
structure
=
color

53. the dance of colors
OHO
OH
O
OH
O O
HO
HO
OH
OH
absorption
wavelength [nm]
450 600 750

54. the dance of colors
OHO
OH
O
OH
O O
HO
HO
OH
OH
absorption
wavelength [nm]
450 600 750
0 180 1.4
20 ps
↵
1.5
d

55. the dance of colors
OHO
OH
O
OH
O O
HO
HO
OH
OH
absorption
wavelength [nm]
450 600 750
0 180 1.4
20 ps
↵
1.5
d

56. the dance of colors
OHO
OH
O
OH
O O
HO
HO
OH
OH
average spectrum & color
absorption
wavelength [nm]
450 600 750
0 180 1.4
20 ps
↵
1.5
d

57. making sense of it
θ

58. making sense of it
0 20 40 60
0 20 40 60
✓
θ

59. making sense of it
θ
φ
optical
gap [eV]
color
θ
φ
θ

60. why multiscaletime[ps]
time[ps]
angle [deg]angle [deg]

61. why multiscaletime[ps]
time[ps]
angle [deg]angle [deg]

62. why multiscaletime[ps]
time[ps]
angle [deg]angle [deg]

63. long-time dynamics & statistics
¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T2
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="8e11Fo3OOvjyqeCgXOX83IFIogU=">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</latexit>

64. long-time dynamics & statistics
T1
T2
¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T2
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="8e11Fo3OOvjyqeCgXOX83IFIogU=">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</latexit>

65. long-time dynamics & statistics
T1
T2
¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T2
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="8e11Fo3OOvjyqeCgXOX83IFIogU=">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</latexit>
¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T2
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="8e11Fo3OOvjyqeCgXOX83IFIogU=">AAADSnichVLBbtNAEN24BYqBNoUDSFxWRK0SNYpsUwSXokpcOBaUtJW6wVqv184qXtvaHVdElpH4pP4HP8AfcOaGeukmMSJJqzCH1cyb3ffmrSbIE6HBcX42rI3Ne/cfbD20Hz1+sr3T3H16qrNCMT5gWZKp84BqnoiUD0BAws9zxakMEn4WjD9M+2eXXGmRpX2Y5HwoaZyKSDAKBvJ3G99JQBUZ0zynbZJJHtMO3iemVNlXTCJFWelWZb/CRKTgO1/6eOlyl0gKoyAqP1dt6HRCwITgfXyESzIb7kLFwbB0u07vTdep5nx9f8ZY/WM3wF/+ulircWCvZfdW2b1Fdu9/7PiAsDADPXdCtJDmKKTP7vaU+6zC+NuCHFuUY+vlcAh+s+X0nFng24lbJy1Ux4nfvCJhxgrJU2AJ1bqkCgRLeGWTQvOcsjGNeclkoEQ8gmWUSq0nMqjw3nQMvdqbgnf1LgqI3g1LkeYF8NR42jO9qEgwZHi6VjgUijNIJiahTAkzD2Yjar4EzPLZtvHorjq6nZx6Pfd1z/t02Dp+X7vdQi/RK9RGLnqLjtFHdIIGiDV+WdvWc+uF9cP6bf2xrudXrUb95hlaio3NG5q3CU8=</latexit>

66. ¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T2
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="8e11Fo3OOvjyqeCgXOX83IFIogU=">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</latexit>
long-time dynamics & statistics
T1
T2
¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T2
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="8e11Fo3OOvjyqeCgXOX83IFIogU=">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</latexit>
¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T2
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="8e11Fo3OOvjyqeCgXOX83IFIogU=">AAADSnichVLBbtNAEN24BYqBNoUDSFxWRK0SNYpsUwSXokpcOBaUtJW6wVqv184qXtvaHVdElpH4pP4HP8AfcOaGeukmMSJJqzCH1cyb3ffmrSbIE6HBcX42rI3Ne/cfbD20Hz1+sr3T3H16qrNCMT5gWZKp84BqnoiUD0BAws9zxakMEn4WjD9M+2eXXGmRpX2Y5HwoaZyKSDAKBvJ3G99JQBUZ0zynbZJJHtMO3iemVNlXTCJFWelWZb/CRKTgO1/6eOlyl0gKoyAqP1dt6HRCwITgfXyESzIb7kLFwbB0u07vTdep5nx9f8ZY/WM3wF/+ulircWCvZfdW2b1Fdu9/7PiAsDADPXdCtJDmKKTP7vaU+6zC+NuCHFuUY+vlcAh+s+X0nFng24lbJy1Ux4nfvCJhxgrJU2AJ1bqkCgRLeGWTQvOcsjGNeclkoEQ8gmWUSq0nMqjw3nQMvdqbgnf1LgqI3g1LkeYF8NR42jO9qEgwZHi6VjgUijNIJiahTAkzD2Yjar4EzPLZtvHorjq6nZx6Pfd1z/t02Dp+X7vdQi/RK9RGLnqLjtFHdIIGiDV+WdvWc+uF9cP6bf2xrudXrUb95hlaio3NG5q3CU8=</latexit>

67. long-time dynamics & statistics
¯(!) ⇡
1
T
Z T
0
(!, R(t))dt
=
T1
T
1
T1
Z T1
0
(!, R(t))dt +
T2
T
1
T1
Z T2
0
(!, R(t))dt + · · ·
⇠
X
c
Pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="M91ZgbXW8xPN06crywZthMBesCw=">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</latexit>
T1
T2
¯(!) ⇠
X
c
pc
1
Tc
Z Tc
0
(!, R(t))dt
<latexit sha1_base64="vsLVGae9qRyObnVbTXfj1X7G4/A=">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</latexit>

68. conformational analysis

69. conformational analysis

70. Conformers population fro
α β
β
conformational analysis

71. conformational analysis
0.25

72. 1 2 3 4 5 6
0.00
0.05
0.10
0.15
0.20
0.25
0.00
0.05
0.10
0.15
0.20
0.25
conformational analysis
0.00
0.05
0.10
0.15
0.20
0.25

73. 1 2 3 4 5 6
0.00
0.05
0.10
0.15
0.20
0.25
0.00
0.05
0.10
0.15
0.20
0.25
conformational analysis
0.00
0.05
0.10
0.15
0.20
0.25

74. conformational analysis
pends on
g density
of the de-
order are
he doping
hermore,
hat takes
Hall bar
antitative
. Novoselov,
Phys. 3,
tt. 98,
09 (2007).
(2008).
ev. Lett. 108,
Science 344,
ys. Rev. Lett.
10).
echnol. 7,
technol. 7,
1959–2007
03 (2013).
optical data on monolayer MoS2. This research was supported by the
Kavli Institute at Cornell for Nanoscale Science and the Cornell
Center for Materials Research [National Science Foundation (NSF)
DMR-1120296]. Additional funding was provided by the Air Force
Office of Scientific Research (FA9550-10-1-0410) and the
Nano-Material Technology Development Program through the National
Research Foundation of Korea funded by the Ministry of Science,
ICT and Future Planning (2012M3A7B4049887). Device fabrication
was performed at the Cornell NanoScale Science and Technology
Facility, a member of the National Nanotechnology Infrastructure
Network, which is supported by NSF (grant ECCS-0335765). K.L.M.
acknowledges support from the NSF Integrative Graduate Education
and Research Traineeship program (DGE-0654193) and the NSF
Graduate Research Fellowship Program (DGE-1144153).
SUPPLEMENTARY MATERIALS
www.sciencemag.org/content/344/6191/1489/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S10
References (34–37)
24 December 2013; accepted 23 May 2014
10.1126/science.1250140
MACHINE LEARNING
Clustering by fast search and find of
density peaks
Alex Rodriguez and Alessandro Laio
Cluster analysis is aimed at classifying elements into categories on the basis of their
similarity. Its applications range from astronomy to bioinformatics, bibliometrics, and pattern
recognition. We propose an approach based on the idea that cluster centers are characterized
by a higher density than their neighbors and by a relatively large distance from points with
higher densities.This idea forms the basis of a clustering procedure in which the number of
clusters arises intuitively, outliers are automatically spotted and excluded from the analysis, and
clusters are recognized regardless of their shape and of the dimensionality of the space in which
they are embedded. We demonstrate the power of the algorithm on several test cases.
lustering algorithms attempt to classify tion. This method allows the finding of nonspheri-
onDecember17,2015emag.orgonDecember17,2015emag.orgonDecember17,2015emag.orgonDecember17,2015emag.orgonDecember17,2015emag.org
he hole side
Lett. 95,
J. W. Kevek
ruitful
rding the
choosing an appropriate threshold can be non-
trivial, a drawback not present in the mean-shift
clustering method (10, 11). There a cluster is de-
fined as a set of points that converge to the same
local maximum of the density distribution func-
where cðxÞ ¼ 1 if x < 0 and cðxÞ ¼ 0 otherwise,
and dc is a cutoff distance. Basically, ri is equal to
the number of points that are closer than dc to
point i. The algorithm is sensitive only to the rel-
ative magnitude of ri in different points, implying
that, for large data sets, the results of the analysis
are robust with respect to the choice of dc.
1 sciencemag.org SCIENCE
SISSA (Scuola Internazionale Superiore di Studi Avanzati),
via Bonomea 265, I-34136 Trieste, Italy.
E-mail: laio@sissa.it (A.L.); alexrod@sissa.it (A.R.)
side, the VHE and the SHE become equivalent on the hole side
owing to the spin-valley coupled valence band.
33. H.-A. Engel, B. I. Halperin, E. I. Rashba, Phys. Rev. Lett. 95,
166605 (2005).
ACKNOWLEDGMENTS
We thank D. C. Ralph for his insightful suggestions and J. W. Kevek
for technical support. We also thank J. Shan for many fruitful
discussions and Y. You for private communications regarding the
choosing an appropriate threshold can be non-
trivial, a drawback not present in the mean-shift
clustering method (10, 11). There a cluster is de-
fined as a set of points that converge to the same
local maximum of the density distribution func-
where c
and dc is
the num
point i. T
ative ma
that, for
are robu
1492 27 JUNE 2014 • VOL 344 ISSUE 6191
SISSA (Scuola Internazionale Superiore di Studi Avanzati),
via Bonomea 265, I-34136 Trieste, Italy.
E-mail: laio@sissa.it (A.L.); alexrod@sissa.it (A.R.)

75. the multi-scale protocol
1. esCmate conformaConal populaCons from long (> 1μs) classical
MD simulaCons in explicit water solvent:
m¨R =
@E
@R
pc =
Tc
T<latexit sha1_base64="STuIG1a7eprxxfFZZ0pJMPslY94=">AAACGXicbVDLSsNAFJ34rPEVdelmsFjcWJIq6KZQEMFlK32BKWEymbRDJw9mJkIJ+RK/wpVrd+LWlQu3+htObBDbelaHc87l3nPdmFEhTfNdW1peWV1bL23om1vbO7vG3n5XRAnHpIMjFvG+iwRhNCQdSSUj/ZgTFLiM9NzxVe737gkXNArbchKTQYCGIfUpRlJJjtEKoO15kUztAMmR68PbDFbq8NT2OcKpHSMuKWLwOvvlf4K2rccOrtSn4baDs7SdOUbZrJo/gIvEKkgZFGg6xqPtRTgJSCgxQ0Kk+R7MSKbbiSAxwmM0JCkOXE6HIzmrokCISeBm8Di/Ssx7ufifd5dI/3KQ0jBOJAmxiijPTxiUEcy/BD3KCZZsogjCnKp7IB4h1VKqX+q66mjNN1ok3VrVOqvWWuflRrNoWwKH4AicAAtcgAa4AU3QARg8gQ/wCb60B+1Ze9Fep9ElrZg5ADPQ3r4BuZOgVw==</latexit>

76. the multi-scale protocol
1. esCmate conformaConal populaCons from long (> 1μs) classical
MD simulaCons in explicit water solvent;
2. for each of the most populated molecular conformers thus
idenCfied, run a 10-20 ps Car-Parrinello quantum MD simulaCon:
m¨R =
*
@ ˆH
@R
+
µ ¨ = ˆH + ⇤<latexit sha1_base64="tP10NdvYr1bk9WuUTj0+cXmi/Wo=">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</latexit>

77. 1. esCmate conformaConal populaCons from long (> 1μs) classical
MD simulaCons in explicit water solvent;
2. for each of the most populated molecular conformers thus
idenCfied, run a 10-20 ps Car-Parrinello quantum MD simulaCon;
3. for each CPMD trajectory thus generated, compute TDDFpT
spectra on the fly ≈ 1ps apart, treaCng the solvent as a dielectric
conCnuum:
the multi-scale protocol
L˜⇢0
n(t) = !n(t)˜⇢0
n(t)
S(!) =
*
X
n
fn(t) ! !n(t)
<latexit sha1_base64="pHAhkVBsNC71sWM+wisODy9r3QU=">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</latexit>

78. 1. esCmate conformaConal populaCons from long (> 1μs) classical
MD simulaCons in explicit water solvent;
2. for each of the most populated molecular conformers thus
idenCfied, run a 10-20 ps Car-Parrinello quantum MD simulaCon;
3. for each CPMD trajectory thus generated, compute TDDFpT
spectra on the fly ≈ 1ps apart, treaCng the solvent as a dielectric
conCnuum:
the multi-scale protocol
L˜⇢0
n(t) = !n(t)˜⇢0
n(t)
S(!) =
*
X
n
fn(t) ! !n(t)
<latexit sha1_base64="pHAhkVBsNC71sWM+wisODy9r3QU=">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</latexit>
THE JOURNAL OF CHEMICAL PHYSICS 142, 034111 (2015)
Self-consistent continuum solvation for optical absorption of complex
molecular systems in solution
Iurii Timrov,1
Oliviero Andreussi,2
Alessandro Biancardi,1
Nicola Marzari,3
and Stefano Baroni1,3,a)
1
SISSA – Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
THE JOURNAL OF CHEMICAL PHYSICS 142, 034111 (2015)
Self-consistent continuum solvation for optical absorption of complex
molecular systems in solution
Iurii Timrov,1
Oliviero Andreussi,2
Alessandro Biancardi,1
Nicola Marzari,3
and Stefano Baroni1,3,a)
THE JOURNAL OF CHEMICAL PHYSICS 142, 034
Self-consistent continuum solvation for optical abs
molecular systems in solution
Iurii Timrov,1
Oliviero Andreussi,2
Alessandro Biancardi,1
Nicola Ma
and Stefano Baroni1,3,a)
1
SISSA – Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 341
2
Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgime

79. 1. esCmate conformaConal populaCons from long (> 1μs) classical
MD simulaCons in explicit water solvent;
2. for each of the most populated molecular conformers thus
idenCfied, run a 10-20 ps Car-Parrinello quantum MD simulaCon;
3. for each CPMD trajectory thus generated, compute TDDFpT
spectra on the fly ≈ 1ps apart, treaCng the solvent as a dielectric
conCnuum:
4. average the spectra within each conformer and over different
conformers:
the multi-scale protocol
Sc (!) =
*
X
n
fn(t) ! !n(t)
+
c
S(!) =
X
c
pc Sc (!)
<latexit sha1_base64="zkKEAfazMZ4lqDsDh6IYxkogMsI=">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</latexit>

80. 1. esCmate conformaConal populaCons from long (> 1μs) classical
MD simulaCons in explicit water solvent;
2. for each of the most populated molecular conformers thus
idenCfied, run a 10-20 ps Car-Parrinello quantum MD simulaCon;
3. for each CPMD trajectory thus generated, compute TDDFpT
spectra on the fly ≈ 1ps apart, treaCng the solvent as a dielectric
conCnuum:
4. average the spectra within each conformer and over different
conformers:
the multi-scale protocol
Multimodel Approach to the Optical Properties of Molecular Dyes in
Solution
Iurii Timrov,†,¶
Marco Micciarelli,†
Marta Rosa,†
Arrigo Calzolari,‡
and Stefano Baroni*,†
†
SISSA − Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
‡
CNR-NANO, Istituto Nanoscienze, Centro S3, Via Campi 213A, 41125 Modena, Italy
Article
pubs.acs.org/JCTC
Multimodel Approach to the Optical Properties of Molecular Dyes in
Solution
Iurii Timrov,†,¶
Marco Micciarelli,†
Marta Rosa,†
Arrigo Calzolari,‡
and Stefano Baroni*,†
†
SISSA − Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
‡
CNR-NANO, Istituto Nanoscienze, Centro S3, Via Campi 213A, 41125 Modena, Italy
ABSTRACT: We introduce a multimodel approach to the
Article
pubs.acs.org/JCTC
ABSTRACT: We introduce a multimodel approach to the
simulation of the optical properties of molecular dyes in
solution, whereby the effects of thermal fluctuations and of
dielectric screening on the absorption spectra are accounted
for by explicit and implicit solvation models, respectively. Ther-
mal effects are treated by averaging the spectra of molecular
configurations generated by an ab initio molecular-dynamics
simulation where solvent molecules are treated explicitly.
Dielectric effects are then dealt with implicitly by computing the spectra upon removal of the solvent molecules and their
replacement with an effective medium, in the spirit of a continuum solvation model. Our multimodel approach is validated by
comparing its predictions with those of a fully explicit-solvation simulation for cyanidin-3-glucoside (cyanin) chromophore in
water. While multimodel and fully explicit-solvent spectra may differ considerably for individual configurations along the
trajectory, their time averages are remarkably similar, thus providing a solid benchmark of the former and allowing us to save
considerably on the computer resources needed to predict accurate absorption spectra. The power of the proposed methodology
is finally demonstrated by the excellent agreement between its predictions and the absorption spectra of cyanin measured at
strong and intermediate acidity conditions.
1. INTRODUCTION
Modeling the optical properties of molecular dyes in solution has
long relied on a static picture, whereby thermal fluctuations are
thoroughly ignored, either by neglecting the effects of the
environment altogether or by accounting for the dielectric
screening of the solvent through some kind of continuum
solvation model (CSM),1
such as the polarizable continuum model
(PCM),2−6
the conductor-like screening model (COSMO),7−10
or
the (revised) self-consistent continuum solvation (SCCS)
model.11−17
In both cases, the optical spectra are often obtained
at the molecular minimum-energy configuration, as computed
in vacuo or in some effective medium. Nevertheless, recent
studies have shown the importance of thermal fluctuations on the
optical properties of solvated dyes.18−23
Thermal fluctuations are
accurately described in molecular solvation models (MSMs), in
which solvent molecules are treated explicitly, i.e. on the same
atomistic ground as the solute (this approach is often referred to
as explicit solvent model). Some of the previous attempts to
account for thermal fluctuations in the optical properties of
solvated molecules were based on molecular dynamics (MD)
utilizing classical force fields accurately targeted to the specific
system(s) of interest.18,21,22
While this approach is apt to cope
with thermal effects on the optical absorption spectra, its prac-
tical implementation is hampered by the limited transferability of
the available force fields, which would require extensive fitting
and validation procedures for each system to be examined. In one
of our previous works19
we introduced an MSM approach to
simulating the optical properties of solvated dyes where the entire
system (solute plus solvent) is treated quantum mechanically and
let evolve according to ab initio (AI) molecular dynamics,24,25
while absorption spectra are computed on-the-fly using time-
dependent density-functional theory (TDDFT)26,27
and aver-
aged along the trajectory. This naturally accounts for both
thermal and dielectric solvation effects on the optical spectra yet
not requiring any unwieldy system-specific fitting or validation.
When it comes to simulating large systems comprising hundreds
of atoms, however, the deployment of ab initio MSMs is hindered
by the large computational cost of hybrid functionals,28−30,32
particularly when using plane-wave basis sets, as it is common
practice in many applications involving AIMD. In a previous
paper23
we proposed to use a GGA exchange-correlation (XC)
energy functional33
to generate explicit-solvent AIMD trajecto-
ries and a semiempirical morphing procedure, tailored on the gas-
phase B3LYP29
TDDFT spectra of the dye, to correct the GGA
spectra evaluated along the AIMD trajectory. GGA is generally
assumed to be accurate enough for the sake of sampling AIMD
trajectories, in spite of the minor, but not always negligible, dif-
ferences existing between the harmonic frequencies computed
using different functionals.31
As for the morphing procedure
previously proposed, while it proved accurate enough to deal
with global properties of the optical spectra, such as the color
expressed by a given solution, it may not be so when it comes to
predicting individual spectral features.
In this paper we propose an approach to this problem that
combines the advantages of CSMs and MSMs, by applying them
Received: April 24, 2016
Published: July 21, 2016
© 2016 American Chemical Society 4423 DOI: 10.1021/acs.jctc.6b00417
J. Chem. Theory Comput. 2016, 12, 4423−4429
DownloadedviaSISSAonSeptember19,2019at11:44:23(UTC).
Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.

81. 1. esCmate conformaConal populaCons from long (> 1μs) classical
MD simulaCons in explicit water solvent;
2. for each of the most populated molecular conformers thus
idenCfied, run a 10-20 ps Car-Parrinello quantum MD simulaCon;
3. for each CPMD trajectory thus generated, compute TDDFpT
spectra on the fly ≈ 1ps apart, treaCng the solvent as a dielectric
conCnuum:
4. average the spectra within each conformer and over different
conformers:
the multi-scale protocol
Multimodel Approach to the Optical Properties of Molecular Dyes in
Solution
Iurii Timrov,†,¶
Marco Micciarelli,†
Marta Rosa,†
Arrigo Calzolari,‡
and Stefano Baroni*,†
†
SISSA − Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
‡
CNR-NANO, Istituto Nanoscienze, Centro S3, Via Campi 213A, 41125 Modena, Italy
Article
pubs.acs.org/JCTC
Multimodel Approach to the Optical Properties of Molecular Dyes in
Solution
Iurii Timrov,†,¶
Marco Micciarelli,†
Marta Rosa,†
Arrigo Calzolari,‡
and Stefano Baroni*,†
†
SISSA − Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
‡
CNR-NANO, Istituto Nanoscienze, Centro S3, Via Campi 213A, 41125 Modena, Italy
ABSTRACT: We introduce a multimodel approach to the
Article
pubs.acs.org/JCTC
ABSTRACT: We introduce a multimodel approach to the
simulation of the optical properties of molecular dyes in
solution, whereby the effects of thermal fluctuations and of
dielectric screening on the absorption spectra are accounted
for by explicit and implicit solvation models, respectively. Ther-
mal effects are treated by averaging the spectra of molecular
configurations generated by an ab initio molecular-dynamics
simulation where solvent molecules are treated explicitly.
Dielectric effects are then dealt with implicitly by computing the spectra upon removal of the solvent molecules and their
replacement with an effective medium, in the spirit of a continuum solvation model. Our multimodel approach is validated by
comparing its predictions with those of a fully explicit-solvation simulation for cyanidin-3-glucoside (cyanin) chromophore in
water. While multimodel and fully explicit-solvent spectra may differ considerably for individual configurations along the
trajectory, their time averages are remarkably similar, thus providing a solid benchmark of the former and allowing us to save
considerably on the computer resources needed to predict accurate absorption spectra. The power of the proposed methodology
is finally demonstrated by the excellent agreement between its predictions and the absorption spectra of cyanin measured at
strong and intermediate acidity conditions.
1. INTRODUCTION
Modeling the optical properties of molecular dyes in solution has
long relied on a static picture, whereby thermal fluctuations are
thoroughly ignored, either by neglecting the effects of the
environment altogether or by accounting for the dielectric
screening of the solvent through some kind of continuum
solvation model (CSM),1
such as the polarizable continuum model
(PCM),2−6
the conductor-like screening model (COSMO),7−10
or
the (revised) self-consistent continuum solvation (SCCS)
model.11−17
In both cases, the optical spectra are often obtained
at the molecular minimum-energy configuration, as computed
in vacuo or in some effective medium. Nevertheless, recent
studies have shown the importance of thermal fluctuations on the
optical properties of solvated dyes.18−23
Thermal fluctuations are
accurately described in molecular solvation models (MSMs), in
which solvent molecules are treated explicitly, i.e. on the same
atomistic ground as the solute (this approach is often referred to
as explicit solvent model). Some of the previous attempts to
account for thermal fluctuations in the optical properties of
solvated molecules were based on molecular dynamics (MD)
utilizing classical force fields accurately targeted to the specific
system(s) of interest.18,21,22
While this approach is apt to cope
with thermal effects on the optical absorption spectra, its prac-
tical implementation is hampered by the limited transferability of
the available force fields, which would require extensive fitting
and validation procedures for each system to be examined. In one
of our previous works19
we introduced an MSM approach to
simulating the optical properties of solvated dyes where the entire
system (solute plus solvent) is treated quantum mechanically and
let evolve according to ab initio (AI) molecular dynamics,24,25
while absorption spectra are computed on-the-fly using time-
dependent density-functional theory (TDDFT)26,27
and aver-
aged along the trajectory. This naturally accounts for both
thermal and dielectric solvation effects on the optical spectra yet
not requiring any unwieldy system-specific fitting or validation.
When it comes to simulating large systems comprising hundreds
of atoms, however, the deployment of ab initio MSMs is hindered
by the large computational cost of hybrid functionals,28−30,32
particularly when using plane-wave basis sets, as it is common
practice in many applications involving AIMD. In a previous
paper23
we proposed to use a GGA exchange-correlation (XC)
energy functional33
to generate explicit-solvent AIMD trajecto-
ries and a semiempirical morphing procedure, tailored on the gas-
phase B3LYP29
TDDFT spectra of the dye, to correct the GGA
spectra evaluated along the AIMD trajectory. GGA is generally
assumed to be accurate enough for the sake of sampling AIMD
trajectories, in spite of the minor, but not always negligible, dif-
ferences existing between the harmonic frequencies computed
using different functionals.31
As for the morphing procedure
previously proposed, while it proved accurate enough to deal
with global properties of the optical spectra, such as the color
expressed by a given solution, it may not be so when it comes to
predicting individual spectral features.
In this paper we propose an approach to this problem that
combines the advantages of CSMs and MSMs, by applying them
Received: April 24, 2016
Published: July 21, 2016
© 2016 American Chemical Society 4423 DOI: 10.1021/acs.jctc.6b00417
J. Chem. Theory Comput. 2016, 12, 4423−4429
DownloadedviaSISSAonSeptember19,2019at11:44:23(UTC).
Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.

82. effects of the environment: acidity
OHO
OH
OH
OH
O O
HO
HO
OH
OH
Cyanidin 3-O-glucoside

83. OHO
OH
OH
OH
O O
HO
HO
OH
OH
effects of the environment: acidity
+
AH+ flavylium cation
-H+
A - quinoidal base
0
OHO
OH
O
OH
O O
HO
HO
OH
OH
HO
OH
O
OH
O O
HO
HO
OH
OH
OH O
Cc - cis-chalcone
HO
OH
O
HO
O
O
HO
HO
OH
OH
OH
O
Ct - trans-chalcone
OHO
OH
O
OH
O O
HO
HO
OH
OH
OH
B - carbinol
+OH-
0

84. OHO
OH
OH
OH
O O
HO
HO
OH
OH
effects of the environment: acidity
+
AH+ flavylium cation
-H+
A - quinoidal base
0
OHO
OH
O
OH
O O
HO
HO
OH
OH
HO
OH
O
OH
O O
HO
HO
OH
OH
OH O
Cc - cis-chalcone
HO
OH
O
HO
O
O
HO
HO
OH
OH
OH
O
Ct - trans-chalcone
OHO
OH
O
OH
O O
HO
HO
OH
OH
OH
B - carbinol
+OH-
0

85. OHO
OH
OH
OH
O O
HO
HO
OH
OH
effects of the environment: acidity
+
AH+ flavylium cation
-H+
A - quinoidal base
0
OHO
OH
O
OH
O O
HO
HO
OH
OH
HO
OH
O
OH
O O
HO
HO
OH
OH
OH O
Cc - cis-chalcone
HO
OH
O
HO
O
O
HO
HO
OH
OH
OH
O
Ct - trans-chalcone
OHO
OH
O
OH
O O
HO
HO
OH
OH
OH
B - carbinol
+OH-
0
OHO
O
O
OH
O O
HO
HO
OH
OH
-
-H+
−

86. OHO
OH
OH
OH
O O
HO
HO
OH
OH
effects of the environment: acidity
+
AH+ flavylium cation
-H+
A - quinoidal base
0
OHO
OH
O
OH
O O
HO
HO
OH
OH
HO
OH
O
OH
O O
HO
HO
OH
OH
OH O
Cc - cis-chalcone
HO
OH
O
HO
O
O
HO
HO
OH
OH
OH
O
Ct - trans-chalcone
OHO
OH
O
OH
O O
HO
HO
OH
OH
OH
B - carbinol
+OH-
0
?
OHO
O
O
OH
O O
HO
HO
OH
OH
-
-H+
−
?

87. OHO
OH
OH
OH
O O
HO
HO
OH
OH
+
comparing predictions with experiments

88. OHO
OH
OH
OH
O O
HO
HO
OH
OH
+
comparing predictions with experiments
450 550 650
λ
experiment

89. OHO
OH
OH
OH
O O
HO
HO
OH
OH
+
comparing predictions with experiments
450 550 650
λ
experiment
450 550 650
λ
theory

90. comparing predictions with experiments
OHO
OH
OH
OH
O O
HO
HO
OH
OH
+
OHO
OH
O
OH
O O
HO
HO
OH
OH
0
450 550 650
λ
experiment

91. comparing predictions with experiments
OHO
OH
OH
OH
O O
HO
HO
OH
OH
+
OHO
OH
O
OH
O O
HO
HO
OH
OH
0
450 550 650
λ
experiment theory
450 550 650
λ

92. OHO
O
O
OH
O O
HO
HO
OH
OH
-
H5
OO
O
OH
O O
HO
HO
OH
OH
-
OH
H7
comparing predictions with experiments
450 550 650
λ
pH=9
pH=8
pH=7
450 550 650
λ
H7
H5

93. OHO
O
O
OH
O O
HO
HO
OH
OH
-
H5
OO
O
OH
O O
HO
HO
OH
OH
-
OH
H7
comparing predictions with experiments
450 550 650
λ
pH=9
pH=8
pH=7
450 550 650
λ
H7
H5
pH9
450 550 650
λ

94. OHO
O
O
OH
O O
HO
HO
OH
OH
-
H5
OO
O
OH
O O
HO
HO
OH
OH
-
OH
H7
comparing predictions with experiments
450 550 650
λ
pH=9
pH=8
pH=7
450 550 650
λ
H7
H5
pH9
450 550 650
λ
Cite this: Phys.Chem.Chem.Phys.,
2019, 21, 8757
Unraveling the molecular mechanisms of color
expression in anthocyanins†
Mariami Rusishvili, ab
Luca Grisanti, ‡a
Sara Laporte, a
Marco Micciarelli, §a
Marta Rosa, ¶a
Rebecca J. Robbins,c
Tom Collins,d
Alessandra Magistrato e
and Stefano Baroni *ae
Anthocyanins are a broad family of natural dyes, increasingly finding application as substitutes for
artificial colorants in the food industry. In spite of their importance and ubiquity, the molecular principles
responsible for their extreme color variability are poorly known. We address these mechanisms by
computer simulations and photoabsorption experiments of cyanidin-3-O-glucoside in water solution, as
a proxy for more complex members of the family. Experimental results are presented in the range of
pH 1–9, accompanied by a comprehensive systematic computational study across relevant charge states
and tautomers. The computed spectra are in excellent agreement with the experiments, providing
unprecedented insight into the complex behavior underlying color expression in these molecules.
Besides confirming the importance of the molecule’s charge state, we also unveil the hitherto unrecognizedReceived 6th February 2019,
PCCP
PAPER
deraCreativeCommonsAttribution3.0UnportedLicence.
View Article Online
View Journal | View Issue

95. in the quest for a natural blue 1
1. bend the CB bond
2. inhibit deprotonation
at 5

96. in the quest for a natural blue 1
450 550 650
λ
5
7
1. bend the CB bond
2. inhibit deprotonation
at 5

97. in the quest for a natural blue 1

98. in the quest for a natural blue 1

99. in the quest for a natural blue 1

100. in the quest for a natural blue 1
θ
φ
θ
φ
θ

101. predicting tautomeric equilibria and pKa
Cy3G+

102. predicting tautomeric equilibria and pKa
H+±
Cy3G (4’)Cy3G+

103. Cy3G (4’)
predicting tautomeric equilibria and pKa
Cy3G+
Cy3G (7)
H+±

104. predicting tautomeric equilibria and pKa
1 1.2 1.4 1.6 1.8 2
0.2
0.1
0
0.1
0.2
0.3
0.4
3.5
3
2.5
2
1.5
1
0.5
0
kcal/mol
deprotonated at 4' deprotonated at 7
Cy3G (4’) Cy3G (7)

105. F =
Z 1
0
⌧
@H(⌘)
@⌘
d⌘
<latexit sha1_base64="ZeyrUaIOqAtyj8Qolb0Nf9GmOpc=">AAACI3icbVDLSgNBEJz1GeMr6tHLYBDiJeyqoBdBVCRHBaOCE0PvpDcZnH0w0yuEkM/xA/wEz97EiwfPXvUP3I0BSbRONVXd9FT5iVaWXPfNmZicmp6ZLcwV5xcWl5ZLK6uXNk6NxLqMdWyufbCoVYR1UqTxOjEIoa/xyr87zv2rezRWxdEFdRNshNCOVKAkUCY1SzfiBDUBP+UHQkXUdG89LjQGJDREbY1cBAZkTyRgSIHmtYpAgq3+r5K/+1wY1e6QMD9LrYHaLJXdqjsA/0u8ISmzIc6apUfRimUaYkRSg7W9/ITU2C+K1GIC8g7a2JOhPzg2qkJobTf0+3wzBOrYcS8X//NuUgr2Gz0VJSlhJLORzAtSzSnmeV+8pQxK0t2MgDQq+w+XHcg6oazVYjHL6I0n+ksut6veTnX7fLd8eDRMW2DrbINVmMf22CGrsTNWZ5I9sQ/2yb6cB+fZeXFef0YnnOHOGhuB8/4NM16kNQ==</latexit>
predicting tautomeric equilibria and pKa
thermodynamic integration
Cy3G (4’) Cy3G (7)

106. predicting tautomeric equilibria and pKa
F =
Z 1
0
⌧
@H(⌘)
@⌘
d⌘
<latexit sha1_base64="ZeyrUaIOqAtyj8Qolb0Nf9GmOpc=">AAACI3icbVDLSgNBEJz1GeMr6tHLYBDiJeyqoBdBVCRHBaOCE0PvpDcZnH0w0yuEkM/xA/wEz97EiwfPXvUP3I0BSbRONVXd9FT5iVaWXPfNmZicmp6ZLcwV5xcWl5ZLK6uXNk6NxLqMdWyufbCoVYR1UqTxOjEIoa/xyr87zv2rezRWxdEFdRNshNCOVKAkUCY1SzfiBDUBP+UHQkXUdG89LjQGJDREbY1cBAZkTyRgSIHmtYpAgq3+r5K/+1wY1e6QMD9LrYHaLJXdqjsA/0u8ISmzIc6apUfRimUaYkRSg7W9/ITU2C+K1GIC8g7a2JOhPzg2qkJobTf0+3wzBOrYcS8X//NuUgr2Gz0VJSlhJLORzAtSzSnmeV+8pQxK0t2MgDQq+w+XHcg6oazVYjHL6I0n+ksut6veTnX7fLd8eDRMW2DrbINVmMf22CGrsTNWZ5I9sQ/2yb6cB+fZeXFef0YnnOHOGhuB8/4NM16kNQ==</latexit>
Cy3G (4’) Cy3G (7)
1 H
λ=0
no H½ H
½ Hno H
1 H
λ=½ λ=1

107. F =
Z 1
0
⌧
@H(⌘)
@⌘
d⌘
<latexit sha1_base64="ZeyrUaIOqAtyj8Qolb0Nf9GmOpc=">AAACI3icbVDLSgNBEJz1GeMr6tHLYBDiJeyqoBdBVCRHBaOCE0PvpDcZnH0w0yuEkM/xA/wEz97EiwfPXvUP3I0BSbRONVXd9FT5iVaWXPfNmZicmp6ZLcwV5xcWl5ZLK6uXNk6NxLqMdWyufbCoVYR1UqTxOjEIoa/xyr87zv2rezRWxdEFdRNshNCOVKAkUCY1SzfiBDUBP+UHQkXUdG89LjQGJDREbY1cBAZkTyRgSIHmtYpAgq3+r5K/+1wY1e6QMD9LrYHaLJXdqjsA/0u8ISmzIc6apUfRimUaYkRSg7W9/ITU2C+K1GIC8g7a2JOhPzg2qkJobTf0+3wzBOrYcS8X//NuUgr2Gz0VJSlhJLORzAtSzSnmeV+8pQxK0t2MgDQq+w+XHcg6oazVYjHL6I0n+ksut6veTnX7fLd8eDRMW2DrbINVmMf22CGrsTNWZ5I9sQ/2yb6cB+fZeXFef0YnnOHOGhuB8/4NM16kNQ==</latexit>
predicting tautomeric equilibria and pKa
CyG (4’) CyG (7)

108. 0 0.5 1
η
F =
Z 1
0
⌧
@H(⌘)
@⌘
d⌘
<latexit sha1_base64="ZeyrUaIOqAtyj8Qolb0Nf9GmOpc=">AAACI3icbVDLSgNBEJz1GeMr6tHLYBDiJeyqoBdBVCRHBaOCE0PvpDcZnH0w0yuEkM/xA/wEz97EiwfPXvUP3I0BSbRONVXd9FT5iVaWXPfNmZicmp6ZLcwV5xcWl5ZLK6uXNk6NxLqMdWyufbCoVYR1UqTxOjEIoa/xyr87zv2rezRWxdEFdRNshNCOVKAkUCY1SzfiBDUBP+UHQkXUdG89LjQGJDREbY1cBAZkTyRgSIHmtYpAgq3+r5K/+1wY1e6QMD9LrYHaLJXdqjsA/0u8ISmzIc6apUfRimUaYkRSg7W9/ITU2C+K1GIC8g7a2JOhPzg2qkJobTf0+3wzBOrYcS8X//NuUgr2Gz0VJSlhJLORzAtSzSnmeV+8pQxK0t2MgDQq+w+XHcg6oazVYjHL6I0n+ksut6veTnX7fLd8eDRMW2DrbINVmMf22CGrsTNWZ5I9sQ/2yb6cB+fZeXFef0YnnOHOGhuB8/4NM16kNQ==</latexit>
predicting tautomeric equilibria and pKa
CyG (4’) CyG (7)

109. F =
Z 1
0
⌧
@H(⌘)
@⌘
d⌘
<latexit sha1_base64="ZeyrUaIOqAtyj8Qolb0Nf9GmOpc=">AAACI3icbVDLSgNBEJz1GeMr6tHLYBDiJeyqoBdBVCRHBaOCE0PvpDcZnH0w0yuEkM/xA/wEz97EiwfPXvUP3I0BSbRONVXd9FT5iVaWXPfNmZicmp6ZLcwV5xcWl5ZLK6uXNk6NxLqMdWyufbCoVYR1UqTxOjEIoa/xyr87zv2rezRWxdEFdRNshNCOVKAkUCY1SzfiBDUBP+UHQkXUdG89LjQGJDREbY1cBAZkTyRgSIHmtYpAgq3+r5K/+1wY1e6QMD9LrYHaLJXdqjsA/0u8ISmzIc6apUfRimUaYkRSg7W9/ITU2C+K1GIC8g7a2JOhPzg2qkJobTf0+3wzBOrYcS8X//NuUgr2Gz0VJSlhJLORzAtSzSnmeV+8pQxK0t2MgDQq+w+XHcg6oazVYjHL6I0n+ksut6veTnX7fLd8eDRMW2DrbINVmMf22CGrsTNWZ5I9sQ/2yb6cB+fZeXFef0YnnOHOGhuB8/4NM16kNQ==</latexit>
predicting tautomeric equilibria and pKa
0 0.5 1
η
0.99 1
CyG (4’) CyG (7)

110. conclusions

111. • the color optical properties of anthocyanins depend
sensitively on intramolecular distortions due to either thermal
fluctuations or co-pigmentation
conclusions

112. • the color optical properties of anthocyanins depend
sensitively on intramolecular distortions due to either thermal
fluctuations or co-pigmentation
• the protomeric state of the negative species also affects the
color, with far-reaching consequences on the bluing effect of
co-pigmenation
conclusions

113. • the color optical properties of anthocyanins depend
sensitively on intramolecular distortions due to either thermal
fluctuations or co-pigmentation
• the protomeric state of the negative species also affects the
color, with far-reaching consequences on the bluing effect of
co-pigmenation
• molecular simulations have been instrumental in the
identification of a natural substitute for blue 1
conclusions

114. • the color optical properties of anthocyanins depend
sensitively on intramolecular distortions due to either thermal
fluctuations or co-pigmentation
• the protomeric state of the negative species also affects the
color, with far-reaching consequences on the bluing effect of
co-pigmenation
• molecular simulations have been instrumental in the
identification of a natural substitute for blue 1
• applied research can be fun and instructive for theoretical
physicists as well …
conclusions

115. Marta
Rosa
Marco
Micciarelli
Alessandro
Laio
Iurii
Timrov
Mariami
Rusishvili
Rebecca
Robbins
Tom
Collins
Luca
Grisanti
Alessandra
Magistrato
Sara
Laporte
thanks to

116. and to

118. save the Amazon,
please!

119. save the Amazon,
please!
http://talks.baroni.me