STUDIES ON TAUTOMERISM Energies and dynamics

Eötvös University, Institute of Chemistry, Laboratory of Theoretical Chemistry,Pf. 32, Budapest, Hungary, H-1518

Results 1. Energies of tautomer pairs and transition states. Watch for the role of water (monohydrate).

Scheme 1. Systems studied: a) acetaldehyde – vinylalcohol; b) acetaldimine – vinylamine;c) formamide – formamidic acid; d) formamidine – formamidine.

References[1] PQS version 2.4, Parallel Quantum Solutions, 2013 Green Acres Road, Fayetteville, AR 72703. Private version from Peter Pulay. [2] ACES II, Mainz-Austin-Budapest version, J.F. Stanton, J. Gauss, J. D. Watts, P. G. Szalay, R. J. Bartlett; with contributions from A.A. Auer, D.B. Bernholdt, O. Christiansen, M.E. Harding, M. Heckert, O. Heun, C. Huber, D. Jonsson, J. Jusélius, W.J. Lauderdale, T. Metzroth, C. Michauk, D.P. O'Neill, D.R. Price, K. Ruud, F. Schiffmann, A. Tajti, M.E. Varner, J. Vázquez and the integral packages MOLECULE (J. Almlöf and P.R. Taylor), PROPS (P.R. Taylor), and ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jorgensen, J. Olsen), [3] Pulay, P., Fogarasi, G.: Fock matrix dynamics, CPL 386, 272-278 (2004)

CONCLUSIONTautomerization is strongly facilitated by water, as studied in form of monohydrates. The TS barrier is lowered by more than a factor of 2. Explicit dynamics calculations capture the mechanism: tautomerization proceeds through a synchronous, concerted process.

Acknowledgement. Financial support has been provided by a Hungarian science grant NKTH-OTKA-A07, no. K 68427.

Central European Symposium on Theoretical Chemistry (CEST-2009), Dobogókő, Hungary, September 25-28, 2009.

Géza Fogarasi

Motivation: an embarrassing DISCREPANCY between theory and experiment about CYTOSINE (logo above).Before continuing with that project, test calculations on small prototype molecules are inevitable.

C C

O

H

H

H H

C C

H

O

H

H

H

C C

N

H

C C

H

N

H

H

H

H

H

H

HH

N C

O

H

H

N C

H

OHH

HH

Table 1A Energies of tautomer pairs (energies E in a.u.= 4.3594 10-18 J, differences in kcal = 4.184 kJ).

Methoda

Acet- aldehyde E+152

Vinyl- alcohol E+152

Acet- aldimine E+132

Vinyl-amine E+132

RHF/3-21G

-0.05344

-0.04177

7.3

-0.32300

-0.32644

-2.1

/6-31G(d,p) -0.92089 -0.90099 12.5 -1.08422 -1.07515 5.7 /6-311G(d,p) -0.95600 -0.93789 11.4 -1.11134 -1.10399 4.6 /6-311++G(2d,2p) -0.96682 -0.94940 10.9 -1.12218 -1.11510 4.4 /6-311++G(3df,3pd) -0.97339 -0.95637 10.7 -1.12670 -1.12016 4.1 B3LYP/3-21G -0.97651 -0.95926 10.8 -1.20964 -1.20991 -0.20 /6-31G(d,p) -1.83393 -1.81605 11.2 -1.96155 -1.95430 4.5 /6-311G(d,p) -1.87494 -1.85968 9.6 -1.99430 -1.98980 2.8 /6-311++G(2d,2p) -1.88574 -1.87187 8.7 -2.00467 -2.00106 2.3 /6-311++G(3df,3pd) -1.89150 -1.87811 8.4 -2.00911 -2.00605 1.9 MP2 /6-31G(d,p) -1.37683 -1.35559 13.3 -1.53274 -1.52199 6.7 /6-311G(d,p) -1.44070 -1.42260 11.4 -1.58039 -1.57192 5.3 /6-311++G(2d,2p) -1.48468 -1.46941 9.6 -1.61982 -1.61415 3.6 /6-311++G(3df,3pd) -1.54358 -1.52941 8.9 -1.67415 -1.66947 2.9 /PVTZ//~ -1.54023 -1.52570 9.1 -1.67071 -1.66515 3.5 /aug-PVTZ//~ -1.55245 -1.53824 8.9 -1.68169 -1.67682 3.1 /PVQZ//aug-PVTZ -1.59286 -1.57904 8.7 -1.71723 -1.71258 2.9 /aug-PVQZ//aug-PVTZ -1.59962 -1.58606 8.5 -1.72288 -1.71868 2.6 /PV5Z//aug-PVTZ -1.60929 -1.59578 8.5 -1.73296 -1.72880 2.6 /aug-PV5Z//aug-PVTZ hf2 hf3 -1.73532 -1.73126 2.6 CCSD//MP2b /aug-PVTZ -1.62372 -1.60943 9.0 -1.76155 -1.75569 3.68 /PVQZ -1.69370 -1.68013 8.5 -1.82416 -1.81887 3.32 /aug-PVQZ -1.69962 -1.68639 8.3 -1.82954 -1.82472 3.02 CCSD(T)//MP2b /aug-PVTZ -1.64965 -1.63562 8.8 -1.78745 -1.78158 3.68 /PVQZ -1.72132 -1.70802 8.3 -1.85169 -1.84636 3.34 /aug-PVQZ -1.72769 -1.71476 8.1 -1.85747 -1.85265 3.02 CCSD(T)//CCSD aug-pVTZ//~ -1.64972 -1.63564 8.8 -1.78749 -1.78162 3.7 PVQZ//aug-pVTZ -1.72142 -1.70806 8.4 -1.85173 -1.84641 3.3

Table 1B Effect of water (in form of a monohydrate) on the energies of tautomer pairs (energies E in a.u.= 4.3594 10-18 J, differences in kcal = 4.184 kJ).

Methoda

Form- amide E+167

Formami-dic acid E+167

F.amide- water

E+244 Eh

F.amidic acid- water E+244 Eh

RHF /6-31G(d,p) -1.94049 -1.92025 12.7 -0.97948 -0.96105 11.6 /6-311G(d,p) -1.98228 -1.96233 12.5 -1.04392 -1.02582 11.4 /6-311++G(2d,2p) -1.99477 -1.97571 12.0 -1.06285 -1.04473 11.4 /6-311++G(3df,3pd) -2.00357 -1.98406 12.2 -1.07405 -1.05555 11.6 B3LYP /6-31G(d,p) -2.89702 -2.87689 12.6 -2.33823 -2.32212 10.1 /6-311G(d,p) -2.94626 -2.92570 12.9 -2.41401 -2.39754 10.3 /6-311++G(2d,2p) -2.95970 -2.94026 12.2 -2.43579 -2.41898 10.5 /6-311++G(3df,3pd) -2.96707 -2.94741 12.3 -2.44546 -2.42849 10.6 MP2 /6-31G(d,p) -2.42114 -2.40148 12.3 -1.66137 -1.64471 10.5 /6-311G(d,p) -2.49439 -2.47634 11.3 -1.77752 -1.76305 9.1 /6-311++G(2d,2p) -2.54620 -2.52793 11.5 -1.85834 -1.84249 9.9 /6-311++G(3df,3pd) -2.61111 -2.59278 11.5 -1.95129 -1.93559 9.9 /PVTZ//~ -2.60545 -2.58737 11.3 -1.94194 -1.92713 9.3 /aug-PVTZ//~ -2.62077 -2.60257 11.4 -1.96581 -1.95022 9.8 /PVQZ//aug-PVTZ -2.66265 -2.64435 11.5 -2.02677 -2.01137 9.7 /aug-PVQZ//aug-PVTZ -2.66931 -2.65096 11.5 -2.03713 -2.02134 9.9 /PV5Z//aug-PVTZ xxx -2.66525 xxx -2.05808 -2.04230 9.9 /aug-PV5Z//aug-PVTZ Xxx -2.66823 xxx -2.06265 -2.04673 10.0 CCSD//MP2b /aug-PVTZ -2.68002 -2.66289 10.7 -2.04476 -2.02949 9.6 /PVQZ -2.75693 -2.73965 10.8 -2.15400 -2.13869 9.6 /aug-PVQZ -2.76391 -2.74647 10.9 -2.16454 -2.14885 9.8 CCSD(T)//MP2b /aug-PVTZ -2.70809 -2.69111 10.6 -2.08278 -2.06808 9.2 /PVQZ -2.78761 -2.76965 11.3 -2.19426 -2.17962 9.2 /aug-PVQZ -2.79428 -2.77703 10.8 -2.20575 -2.19067 9.4

Table 2 Transition state energies for tautomer pairsa Acetaldimin

e- Vinylamine

FormamideFormamidic acid

FormamideFormamidic acid

+ water

Formamidine

Formamidine

Formamidine+water

Formamidine+water

TSE+132 TSE+167 TSE+245 TSE+149 MIN+149 TSE+225 MIN+225 B3LYP /6-31G(d,p) -1.85352 63.2 -2.82338 46.2 -1.30718 19.5 -0.93823 -1.01090 45.6 -1.42801 -1.45367 16.1 /6-311++G(2d,2p) -1.89731 65.1 -2.88299 48.1 -1.40052 22.1 -0.98977 -1.06583 47.7 -1.51551 -1.54350 17.6 /6-311++G(3df,3pd) -1.90249 65.0 -2.89097 47.7 -1.41037 22.0 -0.99666 -1.07186 47.2 -1.52459 -1.55192 17.1 MP2 /6-31G(d,p) -1.41800 65.2

-2.34658 46.8 -0.62557 22.5 -0.48803 -0.56288 47.0 -0.77303 -0.80413 19.5

/6-311++G(2d,2p) -1.51078 64.9 -2.47062 47.4 -0.82158 23.1 -0.59244 -0.66823 47.6 -0.95111 -0.98191 19.3 /6-311++G(3df,3pd) -1.56814 63.6 -2.53860 45.5 -0.91728 21.3 -0.65601 -0.72849 45.5 -1.04242 -1.07047 17.6 /PVTZ//~ -1.56413

(2011 cm-1) 64.7

-2.53331 (1894 cm-1)

45.3 -0.90930 (1610 cm-1)

20.5 -0.64943 (1925 cm-1)

-0.72209 45.6 -1.03150 (xxxx cm-1)

-1.06030 18.1

/aug-PVTZ//~ -1.57572 63.4 -2.54854 45.3 -0.93230 21.0 -0.66421 -0.73684 45.6 -1.05589 -1.08363 17.4 /PVQZ//aug-PVTZ -1.61108 63.7 -2.59031 45.4 -0.99318 21.1 -0.70087 -0.77349 45.6 -1.11101 -1.13936 17.8 /aug-PVQZ//aug-PVTZ -1.61441 65.4 -2.59709 45.3 -1.00312 21.3 -0.70747 -0.77989 45.4 -1.12173 -1.14946 17.4 /PV5Z//aug-PVTZ -1.62547 64.8 -2.61135 46.7 -1.02397 21.4 -0.71972 -0.79218 45.5 -1.14034 -1.16837 17.6 Aug-PV5Z//aug-PVTZ -1.62782 64.9 -2.61443 46.8 -1.02837 21.5 -0.72260 -0.79495 45.4 -1.14484 ci2 CCSD//MP22 /aug-PVTZ -1.64655 68.5 -2.60032 50.0 -1.00453 25.2 -0.72427 -0.80501 50.7 -1.13677 -1.17080 21.3 /PVQZ -1.70889 69.0 -2.67723 50.0 -1.11353 25.4 -0.79316 -0.87403 50.7 -1.23750 -1.27213 21.7 /aug-PVQZ -1.71467 72.1 -2.68423 50.0 -1.12393 25.5 -0.80005 -0.88063 50.6 -1.24856 >8GB /aug-PV5Z -2.71611 50.1 CCSD(T)//MP22 /aug-PVTZ -1.67761 65.2 -2.63290 47.2 -1.04649 22.8 -0.75677 -0.83293 47.8 -1.17819 -1.20886 19.2 /PVQZ -1.74166 65.7 -2.71169 47.1 -1.15793 22.8 -0.82743 -0.90362 47.8 -1.28113 -1.31238 19.6 /aug-PVQZ -1.74788 68.8 -2.71926 47.1 -1.16920 22.9 -0.83486 -0.91075 47.6 -1.29317 >8GB /aug-PV5Z -2.75210 47.1

Results 2. Explicite DYNAMICS calculations

a b

cd

Tautomerization of formamide to formamidic acid by water mediatiion.Six snapshots at time intervals of 5 fs. Method: MP2/6-31G(d,p).

Method: ab initio Born-Oppenheimer dynamics

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.

Procedure [3]1. Start geometry not too far from equilibrium2. The atomic nuclei get a random kick such that the average kinetic energy corresponds to a selected temperature.3. Energy and FORCES calculated from ab initio Quantum Chemistry ‘on the fly’4. Movement of atoms calculated classically5. GOTO 3

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).

Methods1.Standard quantum chemistry, from Hartree-Fock to Coupled Cluster,

CCSD(T), basis sets from 3-21G to aug-cc-pV5Z.2.Ab initio Born-Oppenheimer dynamics, B3LYP and MP2, 6-31G(d,p).

Computer programs used: PQS [1], ACES II [2].

Water may mediate the proton transfer in formamide

TAUTOMERIZATION CAPTURED!