Fogarasi Géza ELTE Kémiai Intézet, Elméleti Kémiai Laboratórium

Szervetlen és Fémorganikus Kémiai, Anyag- és Molekulaszerkezeti Munkabizottságok, Eger-Demjén, 2011. márc. 24-26.

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Fogarasi GézaELTE Kémiai Intézet, Elméleti Kémiai Laboratórium

Izomer átalakulások és konformációs változások

kvantumkémiai vizsgálata biomolekulákban


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Motiváció: Citozin


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Watson and Crick, Nature 1953.

……………………………

The significance of tautomerism was recognized from the beginnings:


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Tautomers - unlike conformers – have completely different electronic structures. At the same time, the energy differences may be as low as for conformers, just a few kcal/mol.Then: can we calculate (relative) energies for different electronic systems with an accuracy of ~ 0.5 kcal/mol?!

(This is realistic for conformers, but quite questionable for tautomers.)

The basic challenge for theory should be realized at the beginning:

Már a relatív energiák számítása is kihívás


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Teszt számítások kis molekulákon

N C

O

H

H

N C

H

OHH

HH

Formamide Formamidic acid

C C

N

H

C C

H

N

H

H

H

H

H

H

HH

Acetaldimine Vinylamine


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Methods

Electronic theory:RHF, B3LYP, MP2, CCSD(T)

Basis sets:from 6-31G(d,p) to 6-311++G(3df, 3pd)

and cc-PVTZ to aug-cc-PV5Z


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Table 1. Computed energies for tautomer pairs (energies, E in a.u.= 4.3594 aJ, differences, E in kcal = 4.184 kJ).

Methoda

Form-amideE+168

Formami-dic acid E+168

E kcal/mol

Acet-aldimineE+132

Vinyl-amineE+132

E kcal/mol

RHF/6-31G(d,p)//~ -0.94049 -0.92025 12.7 -1.08422 -1.07515 5.7

/6-311G(d,p)//~ -0.98228 -0.96233 12.5 -1.11134 -1.10399 4.6

/6-311++G(2d,2p)//~ -0.99477 -0.97571 12.0 -1.12218 -1.11510 4.4

/6-311++G(3df,3pd)//~ -1.00357 -0.98406 12.2 -1.12670 -1.12016 4.1

B3LYP/6-31G(d,p)//~ -1.89702 -1.87689 12.6 -1.96155 -1.95430 4.5

/6-311G(d,p)//~ -1.94626 -1.92570 12.9 -1.99430 -1.98980 2.8

/6-311++G(2d,2p)//~ -1.95970 -1.94026 12.2 -2.00467 -2.00106 2.3

/6-311++G(3df,3pd)//~ -1.96707 -1.94741 12.3 -2.00911 -2.00605 1.9

MP2/6-31G(d,p)//~ -1.42114 -1.40148 12.3 -1.53274 -1.52199 6.7

/6-311G(d,p)//~ -1.49439 -1.47634 11.3 -1.58039 -1.57192 5.3

/6-311++G(2d,2p)//~ -1.54620 -1.52793 11.5 -1.61982 -1.61415 3.6

/6-311++G(3df,3pd)//~ -1.61111 -1.59278 11.5 -1.67415 -1.66947 2.9


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/6-311++G(3df,3pd)//~ -1.61111 -1.59278 11.5 -1.67415 -1.66947 2.9

MP2/PVTZ//~ -1.60545 -1.58737 11.3 -1.67071 -1.66515 3.5

/aug-PVTZ//~ -1.62077 -1.60257 11.4 -1.68169 -1.67682 3.1

/PVQZ//aug-PVTZ -1.66265 -1.64435 11.5 -1.71534 -1.71068 2.9

/aug-PVQZ//aug-PVTZ -1.66931 -1.65096 11.5 -1.72005 -1.71586 2.6

/PV5Z//aug-PVTZ -1.68362 -1.66525 11.5 -1.73122 -1.72704 2.6

/aug-PV5Z//aug-PVTZ -1.68665 -1.66823 11.6 -1.73532 -1.73126 2.6

Table 1. contd1.

Methoda

Form-amideE+168


E kcal/mol

Acet-aldimineE+132

Vinyl-amineE+132

E kcal/mol


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Table 1. contd2.

CCSD//MP2 /PVTZ -1.65928 -1.64223 10.7 --- --- ---

/aug-PVTZ -1.68002 -1.66289 10.7 -1.76155 -1.75569 3.7

/PVQZ -1.75693 -1.73965 10.8 -1.82416 -1.81887 3.3

/aug-PVQZ -1.76391 -1.74647 10.9 -1.82954 -1.82472 3.0

/pV5Z -1.79244 -1.77521 10.8 -1.85439 -1.84949 3.1

/aug-pV5Z -1.79590 -1.77865 10.8 --- --- ---

CCSD(T)//MP2 /PVTZ -1.68576 -1.66895 10.5 --- --- ---

/aug-PVTZ -1.70809 -1.69111 10.6 -1.78745 -1.78158 3.7

/PVQZ -1.78671 -1.76965 10.7 -1.85169 -1.84636 3.3

/aug-PVQZ -1.79428 -1.77703 10.8 -1.85747 -1.85265 3.0

/pV5Z -1.82351 -1.80648 10.7 -1.88293 -1.87802 3.1

/aug-pV5Z -1.82720 -1.81014 10.7 --- --- ---

CCSDT//MP2b /PVTZ -1.68593 -1.66900 10.6 --- ---

Methoda

Form-amideE+168


E kcal/mol

Acet-aldimineE+132

Vinyl-amineE+132

E kcal/mol

a Notations follow standard convention except that in the correlation consistent basis sets “cc” is tacitly assumed, thus omitted for brevity. After the double slash ‘//’ the level of geometry optimization is indicated; ’~’ means optimization at the same level as the energy calculation.b All coupled cluster calculations were done at the MP2/aug-pVTZ geometry.


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Tautomer energy differences with the largest basis sets from above, kcal/mol

RHF DFT MP2 CCSD CCSD(T)

Famid-Facid 12.2 12.3 11.6 10.8 10.7

Acimin-Vinam 4.1 1.9 2.6 3.1 3.1

Bad news: a) the two systems behave differently!! b) CC (coupled cluster) level is needed

Good news: SD and SD(T) essentially the same

Conclusion of high-level test calculations


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CYTOSINE tautomersThe most prominent example of a “multiform” molecule:Five low-energy isomers (three tautomers plus two rotamers)

N3

2N1

6

54

NH2

HO

N3

2N1

6

54

NH2

O O

H

N3

2N1

6

54

NH2

H

N3

2N1

6

54

HO

NH

N3

2N1

6

54

HO

NH

1 2a 2b

3a 3b

H H


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Relative energies of cytosine tautomers, ab initio results

MP2 CCSD CCSD(T) ....MP2, CCSD, CCSD(T) ...

A relatív energiák is nagyon érzékenyek a számítási szintre


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Method1 2b 3a

E Ee E E Ee

HF/6-31G(d,p)a 66.77 -0.21 66.98 67.60 +0.62B3LYP/6-31G(d,p)b --- -0.23 --- --- +0.24B3LYP/truncated pVTZc --- -0.21 --- --- +0.21B3LYP/6-311++G(2d,2p)d 61.65 -0.21 61.86 62.12 +0.25MP2/TZPd 61.94 -0.37 62.31 61.97 -0.35

Zero Point Energies, kcal/mol

aGould et al.6 bKwiatkowski and Leszczynski.9 cKobayashi,29 only the differences listed; f functions omitted from the cc-pVTZ basis set.dpresent work. eRelative to 2b.

Compare HF and MP2!

Kevésbé közismert: a zéruspont-energia érzékenysége


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Theoretical results, e.g.: CCSD(T)[f.c.]/cc-pVTZ// rfg 1 2b 3a1.51 0. 1.49

Watch out, black-box users!:DFT gives a qualitatively different picture!

B3LYP/6-311++G(2d,2p): B3PW91/6-311++G(2d,2p):

-0.54 0. 1.27-0.28 0. 1.74

Compare traditional wf and DFT

1: the “canonical” oxo form; 2b: enol; 3a: imino


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Theoretical resultsCCSD(T)[f.c.]/cc-pVTZ// rfg 1 2b 3a1.51 0. 1.49

Conclusion: the three low-energy tautomers of cytosine are within a range of ~ 2 kcal/mol

And, rotamers: 2a 0.8 kcal/mol above 2b, 3b 2 kcal/mol above 3a


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TSrot

Hvib

TSvib

Gcnucl

Gd

nucl

Ge

tot

Conventional Quantum Chemistrya 1 8.291 64.369 4.023 42.496 -0.802 0.86 2b 8.286 64.566 3.423 43.298 ---- --- 3a 8.295 64.389 4.141 42.393 -0.904 0.83 Density Functional Theoryb 1 8.290 64.060 3.808 42.403 -0.432 -0.97 2b 8.285 64.137 3.457 42.835 --- --- 3a 8.292 64.363 3.594 42.918 +0.083 1.35

Cytosine. Thermodynamic Quantities at T = 298 K, kcal/mol

________________________________________________________________________________________________________________________________________________________________

aGeometries (moments of inertia) from CCSD/TZP, vibrational frequencies from MP2/TZP, electronic energies CCSD(T)/cc-pVTZ. bB3LYP/6-311++G(2d,2p). cTotal Gibbs free energy from nuclear motions, including the constant contributions from translation and Hrot. dRelative to tautomer 2b. e After adding the electronic energies, from Tables 3 and 5, respectively, including the corrections fornon-planarity from Table 4, see also text.

Compare G(1-3a), with CC and DFT!

Az egyensúlyt meghatározó szabadentalpiák


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A protonátmenet mechanizmusa

Transition states

B3LYP/6-31G(d,p) -2.82338 46.2 -0.93823 45.6/6-311++G(2d,2p) -2.88299 48.1 -0.98977 47.7/6-311++G(3df,3pd) -2.89097 47.7 -0.99666 47.2

MP2/6-31G(d,p) -2.34658 46.8 -0.48803 47.0/6-311++G(2d,2p) -2.47062 47.4 -0.59244 47.6/6-311++G(3df,3pd) -2.53860 45.5 -0.65601 45.5/PVTZ//~ -2.53331 45.3 -0.64943 45.6 Imag. frequency (1894 cm-1) (1925 cm-1)/aug-PVTZ//~ -2.54854 45.3 -0.66421 45.6/PVQZ//aug-PVTZ -2.59031 45.4 -0.70087 45.6/aug-PVQZ//aug-PVTZ -2.59709 45.3 -0.70747 45.4/PV5Z//aug-PVTZ -2.61135 45.3 -0.71972 45.5aug-PV5Z//aug-PVTZ -2.61443 45.3 -0.72260 45.4

Tautomer pairs formamide- formamidic acid and formamidine - formamidine

FMD-FAC FIM-FIM

ETS+167 TS ETS+149 TS

H

C

O

N

H

H

H

C

O

N

H

H

1A 1B

Vibrational frequencies at MP2/PVTZ level. Each system has one single imaginary frequency, indicating that the TS is indeed a first order saddle point.

Az energiagátak:


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/aug-PVTZ -2.60032 50.0 -0.72427 50.7/PVQZ -2.67723 50.0 -0.79316 50.7/aug-PVQZ -2.68423 50.0 -0.80005 50.6/PV5Z -2.71257 50.1 -0.82606 50.8/aug-PV5Z -2.71611 50.1

CCSD//MP2

aug-PVTZ -2.63290 47.2 -0.75677 47.8/PVQZ -2.71169 47.1 -0.82743 47.8/aug-PVQZ -2.71926 47.1 -0.83486 47.6/PV5Z -2.74835 47.2 -0.86156 47.8/aug-PV5Z -2.75210 47.1

CCSD(T)//MP2

ETS+167 TS ETS+149 TS

Tautomer pairs formamide- formamidic acid and formamidine – formamidinecontnd.

FMD-FAC FIM-FIM

Conclusion: all barriers are far too high for proton transfer to occur.

TS in cytosine (amine – imine) : ~ 40 kcal/mol


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The effect of water

a) Affects the relative energies

b) Affects the TS barrier

Model: supermolecule water molecule(s) added explicitly

A víz szerepe


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The effect of water: 9 structures investigated


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Citozin-monohidrát komplexekThe favorite binding place is the same in all three tautomers. Optimized structures:


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Dissociation energies of cytosine-monohydrates (stabilization by water), kcal/mol.

Complex

EC

0+ 394 ECW +470

De

0

BSSE

De

2bA -0.068997 -0.372743 10.17 -2.50 7.67

1A -0.065350 -0.371807 11.87 -2.50 9.37

One single water molecule makes the keto form 1 already more stable energetically than the hydroxy form 2b.

The keto form binds water significantly stronger

A vízmolekula kapcsolódásának erőssége


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Test: Formamide plus water, water may mediate proton transfer

The TS barrier: Water as a catalyst

Az átmeneti állapot: a vízmolekula hatása


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Formamide ↔ Formamidic acid Monohydrate Amid.H2O

E+244

a.u.

Acid.H2O

E+244 a.u.

E kcal mol-1

TS.H2O

E+244 a.u.

ETS kcal mol-1

Imagin.Freq. cm-1

B3LYP /6-31G(d,p) -2.33823 -2.32212 10.1 -2.30719 19.4 1549i

/6-311++G(2d,2p) -2.43579 -2.41898 10.5 -2.40052 22.1 1621i

MP2 /6-31G(d,p) -1.66137 -1.64471 10.5 -1.62557 22.5 1646i

/aug-PVTZ//~ -1.96581 -1.95022 9.8 -1.93230 21.0 --

/PVQZ//aug-PVTZ -2.02677 -2.01137 9.7 -1.99318 21.1

CCSD(T) SD/aug-PVTZ -2.04476 -2.02949 9.58 -2.00453 25.2 --

SD(T)/aug-PVTZ -2.08278 -2.06808 9.22 -2.04649 22.8 --

SD/PVQZ -2.15400 -2.13869 9.61 -2.11354 25.4

SD(T)/PVQZ -2.19426 -2.17962 9.18 -2.15793 22.8

For comparison, remember: w/o water it was E ~10.5, ETS ~ 47 kcal

_______________________________________________________________________________________________________


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Quantum Chemical Transition State Barrier for Cytosine.H2O and Cytosine.2H2O

Method Basis set Cyt.H2O Cyt.2H2O

DFT (b3lyp) 6-31G(d,p) 15.8a 15.86-311++G(d,p) 18.1 17.7cc-pVTZ 17.7 17.8

MP2 6-31G(d,p) 18.3 19.36-311++G(d,p) 19.6 19.7cc-pVTZ 17.1 18.0

CCSD(T)//MP2/pVTZ aug-pVDZ 19.5 --cc-pVTZ 18.8 --

aImaginary frequency: 1577 cm-1

Cytosine 1 ↔ 3a TS with water

TS reduced by more than a factor of 2; second H2O indifferent

A citozinban az amino ↔ imino átmenet lehet fontos


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A protonátmenet mechanizmusa: ab initio molekuladinamika

Ab initio simulation of dynamics

The notion of reaction mechanisms is based on the Born-Oppenheimer (B-O) approximation: atoms move on a potential energy surface (PES) defined by the electronic energy as a function of nuclear positions. In the simplest models reactions follow the minimum energy pathway (MEP), going through a transition state (TS). The MEP expressed in mass-weighted Cartesians is referred to as the internal reaction coordinate, IRC. Recent computations have shown that reactions may follow a route totally different from the IRC.(W.L. Hase, Science 2002; M. Dupuis, Science 2003).


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True dynamics calculations require knowledge of the complete PES, and recent methods generate it "on the fly". The well-known Car-Parrinello method is most efficient computationally because the electronic wave function is "propagated", and not optimized, at the trajectory points. As a consequence, the system is moving close to, but not exactly on the B-O surface.

In B-O dynamics, the wave function of a QC method is fully optimized in each step along the trajectory. Energy and first derivatives are determined from ab initio wf, with the atomic movements calculated from them classically. This is the approach adopted here. using Verlet's algorithm.

The QC method was DFT(B3LYP)/3-21G.


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Ab initio simulation of cytosine tautomerization

Note the synchronous change of the relevant N – H bonds


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Bázis + cukor = nukleozidcitidin

Egy lépéssel tovább:


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Konformációs problémák ...

Syn conformation: O4’-C1’-N1-C2 = 59 degB3lyp/6-31G** = -891.164082 , dipole/D = 7.4

Anti conformation: O4’-C1’-N1-C2 = -172 degB3lyp/6-31G** = -891.172737, dipole/D = 6.8 D

A glikozidos kötés körüli forgatás szerint:

= 5.4 kcal/mol


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Conformers in the vicinity of the anti form:

“conf1”: -891.172736dipole/D = 6.85

conf2”: -891.174667 dipole/D = 5.66

= 1.2 kcal/mol


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Pályázati támogatások:Financial support by the Hungarian Scientific Research Foundation (OTKA, Grants No. T68427) is greatfully acknowledged. The European Union and the European Social Fund have provided financial support to the project under the grant no. TAMOP 4.2.1./B-09/KMR-2010-0003.


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Maradékok .....


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The End

Acknowledgement. Financial support has been provided by Hungarian science grants NKTH-OTKA-A07, no. K 68427 and OTKA K72423.


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Molekuladinamika

A modell:

1. egy (v. néhány) egyedi molekula

2. Born-Oppenheimer ab initio dinamika:

A magok klasszikusan (Newton) mozognak, a potenciálfelületet kvantummechanika szerint számítjuk


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A modell (folyt.):

Két út:

a) A potenciálfelületet előre legyártjuk, fittelés

b) Direkt módszer: menet közben, on the fly

A trajektória minden egyes pontjában komplett ab initio számítás - energia és erők


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-(dV/dR) = ma V(R) = Emol (r; R),

E comes from solving the electronic Schröd. eq.

Ri+1 = Ri + vit + 1/2ait

2 + 1/6bit3 + ….

visszafele időben:Ri-1 = Ri - vit + 1/2ait

2 - 1/6bit3 + ….

A két egyenletet összeadva:Ri+1 = 2Ri - Ri-1 +ait

2 + …. Verlet

(note: sebességek nincsenek benne explicite; kinetikus energiához külön számolandók a t alatti elmozdulásokból)

A trajektória:


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April 7-11, 2002 XVIII MCC, Dubrovnik, Croatia June 23-28, 2003 46

Snapshots of configurations: (H2O)6F- ; HF/6-31G*; clockwise from top left : t=0, 0.4, 0.8, 1.2 ps

Tesztpéldák: fluorid-, ill. klorid-ion vízben


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Fig. 5. Snapshots of configurations. Top row (H2O)6Cl- ; Bottom row (H2O)6F- from left to

right: t=0, 0.4, 0.8, 1.2 ps. HF/6-31G* calculations, T=150 K, time step = 0.1 fs. Halogen ions are in shadowed black.


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Statika és dinamika egy példán:

CYTOSINE


44Anyagszerkezet-kutatási Konferencia, Mátrafüred, 2006. május 23-24.

Egy komplex vizsgálat:

CYTOSINE

Why cytosine?

- the biological allure is obvious: DNA

- tautomerism : of general interest for the structural chemist

- genetics: mutations?

challenge for QC: describe completely different electronic arrangements with accuracy ΔE < 1 kcal/mol


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T h e th re e lo w -e n e rg y ta u to m e rs o f c y to s in e

N 3

C 2

N 1

C 6

C 5

C 4

H

O 7

N 8

H

H

H s H a

N 3

C 2

N 1

C 6

C 5

C 4

O 7

N 8

H

H

H s H a

H

N 3

C 2

N 1

C 6

C 5

C 4

H

O 7

N 8

H

H

HH

H

3a1 2b

1: the “canonical” oxo form; 2b: enol; 3a: imino


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High-level quantum chemical calculations have been carried out

in an effort to reinvestigate the relative stabilities of the three

lowest-lying tautomers of cytosine.

Geometries were optimized at the CCSD/TZP level,

electronic energies calculated at CCSD(T)/cc-pVTZ

and vibrational frequencies at MBPT(2)/TZP.

Comparative DFT calculations were also performed.

Part 1: Relative stabilities of free tautomers


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1

2b

3a

methoda

A

B

C

b

A

B

C

b

A

B

C

b

…………………… MP2/TZP; compl. 3866 2016 1326 -0.32 3948 2003 1330 -0.36 3842 2017 1324 -0.48 MP2/cc-pVTZ(-f); compl.d 3897 2027 1335 --e 3972 2012 1337 --e 3877 2028 1332 --e

MP2/cc-pVTZ; plan. 3927 2042 1343 -- 4003 2028 1346 -- 3901 2041 1340 -- MP2/cc-pVTZ; compl. 3925 2041 1343 -0.17 3999 2026 1346 -0.25 3901 2041 1340 0.00 CCSD/TZP; plan. 3871 2024 1329 -- 3958 2009 1333 -- 3845 2022 1325 -- B3LYP/6-311++G(2d,2p); compl. 3882 2026 1331 -0.12 3968 2010 1334 -0.17 3862 2025 1328 0.00 B3PW91/6-311++G(2d,2p); compl. 3901 2034 1337 -0.12 3985 2018 1340 -0.18 3881 2034 1335 0.00 exp.f 3872 2025 1330 -.22 3952 2009 1332 -.18 3848 2026 1328 -.18

Indicating Accuracy:Rotational Constants (MHz) of Three Tautomers of Cytosine

Agreement almost too good to be true ?

a Notation: plan. - optimization in planarity constraint; compl. - complete optimization, without constraint. bInertia defect, = IC - IA - IB , in amu Å2 ;

it is, of course, exact zero for structures with planarity constraint; note that the four digits quoted here for the rotational constants are not sufficient for , which was calculated independently from the cartesian coordinates. cOur earlier results23. dResults by Kobayashi29, the cc-pVTZ basis set was truncated by omitting he f functions; e the optimized structure was non-planar but cannot be reproduced from the four-digit rotational constants. fMicrowave spectroscopic results on a supersonic beam by Brown et al.27


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Methoda

2b

1

3a

Energyb

Ec

Ec

MP2/TZP[full]// ~ -0.118852 2.13 2.93

CCSD/TZP[full]// ~ -0.147123 1.57 1.03

CCSD(T)/TZP[full]// rfg -0.206416 1.82 1.76

MP2[full]/TZ2P// rfg -0.236115 1.88 3.07

CCSD[full]/TZ2P// rfg -0.256296 1.21 1.00

CCSD(T)[full]/TZ2P// rfg -0.324782 1.44 1.66

MP2[f.c.]/cc-pVTZ// rfg -0.206469 2.06 2.96

MP2[full]/cc-pVTZ// ~ -0.334255 1.86 2.97

MP2[full]/cc-pVTZ// ~;nonpl. -0.334640 2.01

} < } 3.21

CCSD[f.c.]/cc-pVTZ// rfg -0.220439 1.21 0.75

CCSD(T)[f.c.]/cc-pVTZ// rfg -0.293754 1.51

1.49

Ab Initio Energies of Three Cytosine Tautomers

a Following general practice, the first part of the notation specifies the level of energy calculation; after the symbol // the level of geometry determination is given; f.c. - frozen core, frozen virtuals; full - no restriction; ~ geometry optimization done at the same level as the energy calculation; rfg - the CCSD/TZP geometry used in the majority of high level energy calculations. All geometry optimizations relevant to thistable were run under planarity constraint, except, as indicated, for the non-planar MP2/cc-pVTZ calculation. bAbsolute energy + 394, in atomic units. c Relative energies with respect to tautomer 2b, in kcal/mol.

Compare 1 and 3a, with MP2 and CC!


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Methoda

2b

1

3a

BLYP/6-31G(d,p) plan. -394.823663 -1.17 -0.05 BLYP/6-311++G(2d,2p) plan. -394.955784 -1.80 -0.10 B3LYP/6-31G(d,p) plan. -394.941360 0.01 1.27 B3LYP/6-311++G(2d,2p) plan -395.065071 -0.62 1.15 B3LYP/6-311++G(2d,2p) compl. -395.065267 -0.54 1.27 B3PW91/6-31G(d,p) plan. -394.793061 0.05 1.58 B3PW91/6-311++G(2d,2p) plan. -394.908793 -0.37 1.62 B3PW91/6-311++G(2d,2p) compl. -394.908994 -0.28 1.74

a In the DFT calculations, geometry and energy were always calculated at the same level Plan. - planarity constraint;compl. - complete optimization (allowing non-planar structure). bAbsolute energy for 2b in atomic units, relative energies with respect to 2b, in kcal/mol.

DFT Energies of Three Cytosine Tautomers

_______________________________________________________


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Conclusions on Part 1:

Methodology (reliability):(a) Basis set: electronic energies are stable within ~0.3 kcal/mol, from TZP upwards.

(b) Electron correlation:, the fluctuation of energies between MBPT(2), CCSD and CCSD(T) is still big, of the order of 1 kcal/mol.

(c) Zero point energies: Relative values differ by up to 1 kcal/mol between HF and MP2

(d) Gibbs free energies: 2 to 3 times larger than the ZPE contributions!Also: the ΔG contributions from nuclear motion are very significant, about half of the relative electronic values.

(e) DFT : relative stabilites are qualitatively different from that obtained by conventional quantum chemistry

Relative stabilities:The amino-oxo and the imino-oxo forms are closely equivalent, and only ~ 0.8 kcal less stable than the amino-hydroxy form.

Noticable is the stability of the imino form!


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2b

1

3a

methodb A B Cc A B Cc A B C

MP2/DZP -470.159567 1.46 6.68 0.28 0.91 5.55 1.51 1.65 3.83 MP2/TZP -470.429944 0.23 no min. 0.73 1.26 no min. 3.24 3.74 5.56 MP2/cc-pVDZ+d -470.198974 0.39 no min. -0.20 0.47 no min. 2.35 2.54 4.47 CCSD(T)/TZP//MP2/cc-pVDZ+ -470.372743 0.27 no min. 0.59 1.41 no min. 2.20 3.00 4.38

Additional calculations on selected complexese MP2/cc-pVTZ -470.687284 0.77 0.51 3.06 ? ?

MP2/aug-cc-pVTZf//MP2/cc-pVTZ -470.592165 0.15 -0.44 2.22 ? ?

MP2/cc-pVQZ//MP2/cc-pVTZ -470.713817 0.58 0.07 2.73 ? ?

Zero point energiesg

MP2/TZP 0.124772 -0.17 -0.23 ? ?

Energies of cytosine-monohydrate complexesa

aThe bold letters 1, 2b and 3a refer to three tautomers, and A,B,C to three complexes for each tautomer, see Scheme 1. Electronic energies: for 2bA the absolute energy in hartrees; for the other tautomers, values relative to 2bA in kcal/mol. bUnless otherwise specified, energies refer to the optimum geometry of the given method. . cno min.: search was done but no minimum found for complex C. dcc-pVDZ+: the aug-cc-pVDZ basis set, with a small reduction: the diffuse functions are applied on all heteroatoms and the hydrogens attached to heteroatoms, but are omitted on the carbons and the two C-H hydrogens. eCalculated only for the three tautomers as listed.fThe full augmented cc-pVTZ basis set, with diffuse functions on all atoms; electron correlation with frozen core. gAbsolute energies, in hartrees.

Favorite binding at position A in all 3 cases


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Conclusion on part 2:

1. For all three tautomers, the favorite binding position of water is the O=C2-N1-H moiety (H-O- C2= N1 in the enol form).

2. Water binds to the keto form of cytosine significantly stronger (~ 1.7 kcal/mol) than to the enol form. This may just be enough to reverse the energy ordering of the keto and enol forms.

3. Methodology (strategy for future):

a) take E for tautomers from highest-level electron correlation calculations (very expensive);

b) add E for binding with water from MP2 (DFT?), but basis set should be fairly large.


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Method: ab initio dynamics*

1) cytosine alone

2) can water help?

* Pulay, P., Fogarasi, G.: Fock matrix dynamics, CPL 386, 272-278 (2004)

Part 3:Try to ‘see’ the process of

tautomerisation

Jön végre dinamika is?


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N3

N1

N8

O

H13 H14

H

O9

H16

H15N3

N1O

N8

H

H14O9

H16

H13

H15

A víz közvetíthet:


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Figure 2. Snapshots from the tautomerization trajectory. Total time span 5 ps, with resolution of 1 fs (5000 steps). Shown are steps from

1535 to 1570 fs taken from the original trajectory, every 5th geometry reproduced.


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Movie ??


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The End


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Következő képek: Maradékok ....


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University of California at Davis: The Double Helix Sculpture


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Present study, HF/6-31G*, E= -772.759459 a.u. = -2.3 kcal/mol


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Energy Differences Between Non-Planar and PlanarOptimizations, kcal/mol

Method 1 2b 3a

MP2/TZP -0.64 -0.83 -0.06MP2/cc-pVTZ -0.09 -0.24 ----a

Conclusion: Larger basis sets move the structure towards planarity?


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Relative energies of cytosine tautomers, DFT results

S1 - BLYP, plan.; S2 - B3LYP, plan.; S3 - B3PW91 plan.; S4 - BLYP, plan; S5 - B3LYP, plan; S6 - B3LYP, compl.; S7 - B3PW91, plan.; S8 - B3PW91, compl.


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tautomer T= 200 K T= 298 K T= 470 K T= 570 K

1 0.07 0.23 0.59 0.782b 1.00 1.00 1.00 1.003a 0.07 0.24 0.64 0.862ab 0.15 0.29 0.45 0.52

Calculated Mole Ratiosa

aRelative to tautomer 2b, as obtained from the conventional quantum chemistry calculationsof Gibbs free energies; for details see the footnotes to Table 7. bcalculated from electronic energies only, the latter taken from earlier lower level results, see text


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complex EX0 + 394 EY

0 +76 EXY +470 0 BSSE

2bA -0.068997 -0.287540 -0.372743 10.17 -2.50 7.67

1A -0.065350 -0.287540 -0.371807 11.87 -2.50 9.37

1B -0.065350 -0.287540 -0.370501 11.05 -2.15 8.90

Dissociation energies of cytosine-monohydrate complexesa

a EX0 and EY

0 refer to the corresponding tautomer and to water, respectively, as the monomers, their geometries optimized by MP2/diffs1 and energies calculated at CCSD(T)/TZP; energies in hartrees. 0 is the dissociation

energy without basis set superposition error, is the final value after BSSE correction, all in kcal/mol.

_______________________________________________________


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Tautomerization captured! Time range: 1530-1570 fs ( cf: T 0.1 fs for an X-H str.)


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E(monomers) a E(complexes) - E(monomers)b

Type of calculationc 2b 1 3a 1A – 2bA

3aA – 2bA

1B – 2bB

3aB – 2bB

MP2/cc-pVDZ+ -393.917650 1.51 2.71 -1.71 -0.36 -1.43 -0.56

CCSD/TZP[fc]//MP2/cc-pVDZ+ -394.009551 2.09 2.09 -1.77 -0.85 -1.19 0.08

CCSD(T)/TZP[fc]//MP2/cc-pVDZ+ -394.068997 2.29 2.90 -1.70 -0.70 -0.70 -0.17

MP2/cc-pVTZ -394.334640 2.01 3.21 -1.50 -0.15 - - - -

MP2/aug-cc-PVTZ[fc]//MP2/cc-pVTZ -394.246299 1.57 2.99 -2.01 -0.77 - - - -

B3-LYP/6-311++G(2d,2p) -395.065267 -0.54 1.27 -1.55 -0.26 -0.71 0.20

Monomer energies, and differences in binding energies of cytosine-water complexes

a Absolute energy in hartrees for 2b; for the rest, energy differences in kcal/mol. bEnergy difference of a pair of complexes (from Table 1) minus the energy difference of the corresponding monomer pair from this table. c Where not specified,

geometries were optimized at the same level as energies calculated; calculations marked with [fc] used frozen core in the


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The three lowest-lying tautomers of cytosine were considered, with the water molecule at three different positions for each, thus giving a total of 9 monohydrated structures. Geometries were optimized at the MP2/cc-pVDZ+ level, energies calculated at CCSD(T)/TZP. Zero point energies for the most important three structures were obtained at MP2/TZP.

In the structures investigated, water is attached to the ring by two hydrogen bonds, in one of them water is proton donor, in the other it is proton acceptor. There are two types of structure of this kind. A third type of structure in which water is double proton donor was reported in some earlier studies; according to the present results this structure is an artifact obtained only with small basis sets.

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