1. 1

2. 2 TAUTOMERISM: a special form of isomerism, intermolecular proton transfer Prototype case: Challenge for theory: completely different electronic structures!

3. 3 Motivation: Theoretical studies on CYTOSINE The role of the four bases in DNA …..

4. 4 1: the “canonical” oxo form; 2b: enol; 3a: imino 12b3a 1.51 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

5. 5 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!!

6. 6 Check the reliability of several methods on small molecules. Test calculations on three systems: Section 1. Test calculations

7. 7 Acetaldehyde Vinylalcohol

8. 8 AcetaldimineVinylamine

9. 9 FormamideFormamidic acid

10. 10 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

11. 11 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 Test 1.

12. 12 Table 1. Contnd. Acetaldehyde – Vinylalcohol Tautomer Pair C Geometry selected as standard: MP2/aug-PVTZ

13. 13 Test 2. Acetaldimine - Vinylamine pair, incl. Trans. State _________________________________________ a Energy relative to vinylamine

14. 14 Acetaldimine - Vinylamine contnd. ______________________________________________________ a Energy relative to vinylamine. b At MP2/aug-PVTZ geometry.

15. 15 Formamide – Formamidic acid Test 3.

16. 16 Formamide – Formamidic acid, contnd.

17. 17 Section 2. The effect of water Model: supermolecule a water molecule added explicitly

18. 18 Formamide plus water: water may mediate proton transfer

19. 19 (Formamide – Formamidic acid) Monohydrate

20. 20 CONCLUSIONS ON THE TESTS: _________________________________________________________________ Even the best results are uncertain to ~ 1 kcal/mol

21. 21 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

22. 22 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

23. 23 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).

24. 24 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).

25. 25 Call PQS to show dynamics Two different cases: 601c and 604c

26. 26 The End