1

TAUTOMERISM

in small molecules modelling nucleobases:

structure of isomers and dynamics of proton transfer

Géza Fogarasi

Department of Theoretical Chemistry, Eötvös L. University,

H-1518, Pf. 32, Budapest/Hungary.

7th European Conference on Computational Chemistry, EUCO CC7, Venezia, 11th-15th Sept. 2008.

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TAUTOMERISM:

a special form of isomerism, intermolecular proton transfer

Prototype case:

C C

O

H

H

H H

C C

H

O

H

H

H

Challenge for theory: completely different electronic structures!

3

Motivation: Theoretical studies on CYTOSINE

The role of the four bases in DNA …..

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T h e t h r e e l o w - e n e r g y t a u t o m e r s o f c y t o s i n e , w i t h e n e r g i e s w i t h i n a r a n g e o f ~ 2 k c a l / m o l

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

1 2b 3a1.51 0. 1.49

Theoretical results, e.g.: CCSD(T)[f.c.]/cc-pVTZ// rfg

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

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What about experiment?

From molecular beam MW and noble-gas matrix IR, no reliable quantitative results, but the picture is:

Abundancies (for isolated specii): 2b > 1 >> 3a

Thus, serious discrepancy between theory and experiment!!

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Check the reliability of several methodson small molecules.

Test calculations on three systems:

Section 1. Test calculations

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Acetaldehyde Vinylalcohol

C C

O

H

H

H H

C C

H

O

H

H

H

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Acetaldimine Vinylamine

C C

N

H

C C

H

N

H

H

H

H

H

H

HH

C C

O

H

H

H H

C C

H

O

H

H

H

9

N C

O

H

H

N C

H

OHH

HH

Formamide Formamidic acid

C C

O

H

H

H H

C C

H

O

H

H

H

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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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Method a Acetaldehyde E+152b

Vinylalcohol E+152 b

kcal mol-1

RHF/3-21G -0.05344 -0.04177 7.32 /6-31G(d,p) -0.92089 -0.90099 12.5 /6-311G(d,p) -0.95600 -0.93789 11.4 /6-311++G(2d,2p) -0.96682 -0.94940 10.9 /6-311++G(3df,3pd) -0.97339 -0.95637 10.7 B3LYP/3-21G -0.97651 -0.95926 10.8 /6-31G(d,p) -1.83393 -1.81605 11.2 /6-311G(d,p) -1.87494 -1.85968 9.6 /6-311++G(2d,2p) -1.88574 -1.87187 8.7 /6-311++G(3df,3pd) -1.89150 -1.87811 8.4 MP2 /6-31G(d,p) -1.37683 -1.35559 13.3 /6-311G(d,p) -1.44070 -1.42260 11.4 /6-311++G(2d,2p) -1.48468 -1.46941 9.6 /6-311++G(3df,3pd) -1.54358 -1.52941 8.9

a In calculations with Pople-type basis sets (6-31…) geometries and energies calculated at the same level. b E in atomic units.

Acetaldehyde – Vinylalcohol Tautomer Pair

C C

O

H

H

H H

C C

H

O

H

H

H

Test 1.

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MP2 /PVTZ//PVTZ -1.54023 -1.52570 9.1 /aug-PVTZ//aug-PVTZ -1.55245 -1.53824 8.9 /PVQZ//aug-PVTZ -1.59286 -1.57904 8.7 /aug-PVQZ//aug-PVTZ -1.59962 -1.58606 8.5 CCSD//MP2c /aug-PVTZ -1.62372 -1.60943 9.0 /PVQZ -1.69370 -1.68013 8.5 /aug-PVQZ -1.69962 -1.68639 8.3 CCSD(T)//MP2c /aug-PVTZ -1.64965 -1.63562 8.8 /PVQZ -1.72132 -1.70802 8.3 /aug-PVQZ -1.72769 -1.71476 8.1 CCSD(T)//CCSD(T) aug-pVTZ/ aug-pVTZ -1.64972 -1.63564 8.8 PVQZ//aug-pVTZ -1.72142 -1.70806 8.4

Table 1. Contnd. Acetaldehyde – Vinylalcohol Tautomer Pair

C Geometry selected as standard: MP2/aug-PVTZ

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Test 2.

Acetaldimine - Vinylamine pair, incl. Trans. StateC C

N

H

C C

H

N

H

H

H

H

H

H

HH

ACDIM

E+132

VINAM

E+132

kcal mol-1

TSa

E+132

kcal mol-1

RHF/3-21G -0.32300 -0.32644 -2.16 /6-31G(d,p) -1.08422 -1.07515 5.69 /6-311G(d,p) -1.11134 -1.10399 4.62 /6-311++G(2d,2p) -1.12218 -1.11510 4.44 /6-311++G(3d,3p) -1.12299 -1.11537 4.78 /6-311++G(3df,3pd) -1.12670 -1.12016 4.10 B3LYP/3-21G -1.20964 -1.20991 -0.17 /6-31G(d,p) -1.96155 -1.95430 4.55 -1.85352 63.2 /6-311G(d,p) -1.99430 -1.98980 2.83 /6-311++G(2d,2p) -2.00467 -2.00106 2.26 -1.89731 65.1 /6-311++G(3df,3pd) -2.00911 -2.00605 1.92 MP2 /6-31G(d,p) -1.53274 -1.52199 6.74 -1.41800 /6-311G(d,p) -1.58039 -1.57192 5.31 /6-311++G(2d,2p) -1.61982 -1.61415 3.56 -1.51078 64.9 /6-311++G(3df,3pd) -1.67415 -1.66947 2.93

_________________________________________

a Energy relative to vinylamine

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Acetaldimine - Vinylamine contnd.C C

N

H

C C

H

N

H

H

H

H

H

H

HH

ACDIM

E+132

VINAM

E+132

kcal mol-1

TSa

E+132

kcal mol-1

MP2 /PVTZ//~ -1.67071 -1.66515 3.49 /aug-PVTZ//~ -1.68169 -1.67682 3.06 -1.57572 63.4 /PVQZ//aug-PVTZ -1.71723 -1.71258 2.92 -1.61108 63.7 /aug-PVQZ//aug-PVTZ -1.72288 -1.71868 2.64 -1.61441 65.4 /PV5Z//aug-PVTZ -1.73296 -1.72880 2.61 -1.62547 64.8 /aug-PV5Z//aug-PVTZ -1.73532 -1.73126 2.55 CCSD//MP2b /aug-PVTZ -1.76155 -1.75569 3.68 -1.64655 68.5 /PVQZ -1.82416 -1.81887 3.32 -1.70889 69.0 /aug-PVQZ CCSD(T)//MP2b /aug-PVTZ -1.78745 -1.78158 3.68 -1.67761 65.2 /PVQZ -1.85169 -1.84636 3.34 -1.74166 65.7 CCSD(T)//CCSD(T) aug-pVTZ//~ -1.78749 -1.78162 3.68 … … PVQZ//aug-pVTZ -1.85173 -1.84641 3.34 … …

______________________________________________________ aEnergy relative to vinylamine. bAt MP2/aug-PVTZ geometry.

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Formamide – Formamidic acid

Test 3.

FAMID

E+167

FACID

E+167

kcal mol-1

TS4

E+167

kcal mol-1

RHF/3-21G -0.98490 -0.95683 17.6 /6-31G(d,p) -1.94049 -1.92025 12.7 /6-311G(d,p) -1.98228 -1.96233 12.5 /6-311++G(2d,2p) -1.99477 -1.97571 12.0 /6-311++G(3d,3p) -1.99706 -1.97811 11.9 /6-311++G(3df,3pd) -2.00357 -1.98406 12.2 B3LYP/3-21G -1.94765 --- /6-31G(d,p) -2.89702 -2.87689 12.6 -2.82338 46.2 /6-311G(d,p) -2.94626 -2.92570 12.9 /6-311++G(2d,2p) -2.95970 -2.94026 12.2 /6-311++G(3df,3pd) -2.96707 -2.94741 12.3 MP2 /6-31G(d,p) -2.42114 -2.40148 12.3 -2.34658 46.8 /6-311G(d,p) -2.49439 -2.47634 11.3 /6-311++G(2d,2p) -2.54620 -2.52793 11.5 /6-311++G(3df,3pd) -2.61111 -2.59278 11.5

N C

O

H

H

N C

H

OHH

HH

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Formamide – Formamidic acid, contnd.

MP2 /PVTZ//~ -2.60545 -2.58737 11.3 /aug-PVTZ//~ -2.62077 -2.60257 11.4 -2.54854 45.3 /PVQZ//aug-PVTZ -2.66473 -2.64435 12.8 /aug-PVQZ//aug-PVTZ -2.67326 -2.65096 14.0 /PV5Z//aug-PVTZ -2.68580 -2.66525 12.9 /aug-PV5Z//aug-PVTZ -2.68897 -2.66823 13.0 CCSD//MP22 /aug-PVTZ -2.68002 -2.66289 10.7 -2.60032 50.0 /PVQZ -2.75693 -2.73965 10.8 /aug-PVQZ -2.76391 -2.74647 10.9 CCSD(T)//MP22 /aug-PVTZ -2.70809 -2.69111 10.6 -2.63291 47.2 /PVQZ -2.78761 -2.76965 11.3 … … /aug-PVQZ -2.79428 -2.77703 10.8 … …

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Section 2. The effect of water

Model: supermolecule a water molecule added explicitly

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Formamide plus water: water may mediate proton transfer

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(Formamide – Formamidic acid) Monohydrate

Amid.H2O

E+244 a.u.

Acid.H2O

E+244 a.u.

kcal mol-1

TS.H2O

E+244 a.u.

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

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CONCLUSIONS ON THE TESTS:Electron correlation

Pople’s type 6-311++G(3df,3dp)

Correlation consistent

pVQZ(aug-pVQZ)

RHF DFT MP2 MP2 CCSD CCSD(T)

Ac.ald-Vinylalc

10.7 8.4 8.9 8.7 (8.5)

8.5 (8.3)

8.3 (8.1)

Ac.imine- Vinylam

4.1 1.9 2.9 2.9 (2.6)

3.3 3.3

Formamide-F.acid

12.2 12.3 11.5 12.8 (14.0)

10.8 (10.9)

11.3 (10.8)

Hydrate (10.5) 9.7 9.6 9.2

Basis sets, at MP2

pVTZ aug-pVTZ

pVQZ aug- pVQZ

pV5Z aug- pV5Z

Ac.imine- Vinylam

3.5 3.1 2.5 2.6 2.61 2.55

Formamide-F.acid

11.3 11.4 12.8 14.0 12.9 13.0

_________________________________________________________________

Even the best results are uncertain to ~ 1 kcal/mol

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Formamide - Formamidic acid Monohydrate

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

blue: TS, magenta: acid

E-E

(am

ide)

, kc

al/m

ol

1: b3lyp/31Gdp, 2: b3lyp/311G++2d2p, 3: MP2/31Gdp, 4: MP2/aug-PVTZ, 5: MP2/PVQZ, 6: CCSD/aug-PVTZ, 7: CCSD(T)/aug-PVTZ,

8: CCSD/PVQZ, 9: CCSD(T)/PVQZ

The special case of formaldehyde-hydrate: b3lyp/631G(d,p) works reasonably, as compared to “best”: 10.1 vs. 9.2, 19.4 vs. 22.8

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Method: ab initio dynamics*

Contrary to Car-Parrinello, the wave function is

truly recalculated at each point ….

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

Section 3: Dynamics:Try to ‘see’ the process of tautomerization

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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, and atomic movements calculated from them classically. This is the approach adopted here using Verlet's algorithm.22

The QC method was DFT(B3LYP)/6-31G** and

/6-311++(2d,2p).

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Call PQS to show dynamics

Two different cases:601c and 604c

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The End