New questions aboutTautomerism in Cytosine

Quantum chemical and matrix isolation spectroscopic studies

Géza Fogarasi Research Laboratory of Theoretical Chemistry, Eötvös L. University, H-1518, Pf. 32, Budapest/Hungary.

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Nucleic acid bases are the most conspicuous examples of tautomerism.

1. Background and motivation

The double helix of DNA is fixed by H-bonds, based onspecific tautomeric forms of the bases

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Example: the H-bonds between cytosine and guanine

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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.)

However, the basic challenge for theory should be realized at the beginning:

For the structural chemist, very first question:energy differences

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2. Test calculations, relative energies

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 10-18 J, 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

Formami-dic acid E+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

Formami-dic acid E+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 highest level test calculations

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

N3

2N1

6

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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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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

Summary of extensive calculations

Relative energies

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

Gdnucl

Getot

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

The effect of entropy: differences between tautomers made even smaller (T = 298 K, kcal/mol)

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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.

Note again the failure of DFT!

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4. The mechanism of intramolecular proton transfer 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 have been calculated at the MP2/PVTZ level. Each system has one single imaginary frequency, indicating that the TS is indeed a first order saddle point.

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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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5. The effect of water

a) Affects the relative energies

b) Affects the TS barrier

Model: supermolecule water molecule(s) added explicitly

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a) Relative energies of cytosine-monohydratesQuestions:1) favorite binding positions?2) binding energy difference between tautomers?

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The 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

1B -0.065350 -0.370501 11.05 -2.15 8.90

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

The keto form binds water significantly stronger

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Test: Formamide plus water, water may mediate proton transfer

b) The TS barrier: Water as a catalyst

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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 ~ 45 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 reduces by more than a factor of 2; second H2O indifferent

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6. The elusive question of cytosine tautomers

Solid state and aqueous solution: general agreement that only the “canonical” keto form is present

In the gas phase, however: hydroxy form dominates

(experimental and theoretical information)

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Experimental data (spectroscopy)(temperature poorly defined, 200-300 oC)

Estimated ratios foramino-hydroxy : amino-oxo : imino-oxo (2 : 1 : 3a)

Matrix isolation IR Radchenko, .. Blagoi, 1984Nowak, Lapinski, Fulara 1989Szczesniak, .. Person, 1988

Theor., from G above

Molecular beam MW Brown et al., 1989

1.0 (b rotam. only) : 1.0 : 0.25

1.0(b+a rotam) : 0.5 : 0.1

1.0 : 0.4 : 0.4

Discrepancy about the “rare”imino form

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Experimental details Cytosine sample from Sigma-Aldrich (solid sample, 99% purity), evaporation at 155 oC, matrix: Argon (99.9997%) and Krypton (99.998%). UV Spectrometer: Varian Cary 3E UV-VIS (1 nm resolution), IR spectrometer: Bruker FTS 55 (1 cm-1 resolution).

Own experiments 1.: matrix isolation IR spectrum

C1(keto):1730 (C=O)1660 (C=C)

C3a(imino):1680 (C=N)

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X-H stretching range

C2b(enol)3620 (O-H)

C3a(imino):3490 (N1-H) 3440 (N3-H)

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Disturbing results in the literature ….

1. Previous UV spectra restricted to solid state or solutionAll interpretations based on the keto form.

2. Sophisticated, elegant new, multiphoton experimentsin the gas phase (molecular beams) yield contradictory results.

UV and ionization spectra

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Method

Electronic excited states: Equation of Motion Coupled Cluster (EOM-CC)

Vibrational structure: Linear Vibronic Coupling (LVC)

Theoretical calculation of the UV spectrum

While previous computations were restricted to vertical excitations, we have performed the first simulation of the complete spectrum of cytosine, using the Linear Vibronic Coupling (LVC) method.[12] In this method the full (electronic and nuclear) wave function is evaluated as a coordinate-dependent combination of the excited electronic wave functions at a reference geometry, normally the ground state equilibrium. The calculations require the derivatives of the excited state energy with respect to the ground state normal coordinates. The nuclear wave functions are expanded in the harmonic oscillator basis of the ground state. We used in the LVC model the four lowest excited electronic states (Table 1) and fourteen vibrational modes with several quanta on each of them.

We have carried out extensive calculations on all three tautomers

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Own experiments 2.: matrix isolation UV spectrum

intensity

energy (eV)

Theory:keto form only

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Theory:Mixture of 3 tautomers

energy (eV)

intensity

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Theory: keto only Theory: mixture

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Given that crystalline cytosine contains only the keto form the basic question is: how do the tautomers form under the experimental circumstances? As mentioned above, all quantum chemical calculations predict a high barrier of about 40 kcal/mol for unassisted transformation of cytosine monomer. Traces of water may play a crucial role as water reduces the barrier by about a half. In addition, the interesting possibility of bimolecular tautomerization was brought up recently by Rodgers.

We have made our own calculations to test this idea. Three H-bonded forms of 1:1 are shown in Fig. 3. From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a. Each tautomerization has its own transition state barrier as indicated under the picture.

How may tautomers form during experiments?

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: 6.3, : 4.9, : 7.7

Three H-bonded dimers derived from 1.

From dimer a new dimer 2b:3a can be derived, leads to 2b:2b and to 3a:3a. The lowest TS leads to the hydroxy form 2b. The transition states which lead, partly or fully, to the imino form 3a lie significantly higher. Thus, this model may explain why the imino form appears in the gas state with much smaller abundance than expected.

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7. The mechanism of proton transferAb 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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Movies …

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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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Before drawing conclusions, we have to carefully analyze the available experimental information. Among numerous studies on

cytosine, the UV spectrum in trimethylphosphate solution[8], in films[9] and for single crystal and aqueous solution[10] are of special interest for the present work. All spectra show broad, envelop-type bands; thus, the major question has been one of the number of individual electronic transitions. Although the deconvolution seems rather uncertain, it is common in all studies that the UV spectrum is

discussed in terms of four electronic transitions. Specifically, a classic circular dichroism (CD) study on cytosine-nucleosides from Eyring's group[11] relates the spectrum to benzene: "The results give […] conclusive evidence for four electronic transitions in the cytosine bases above 190 nm which may be related to the B2u, B1u and E1u bands of benzene." Other studies relied on semiempirical quantum chemical calculations to resolve the spectrum.[9b] A linear dichroism (LD) study on the single crystal gave better resolution of the absorption bands by making use of the variation of intensities as a function of the polarization direction.[10] Also, the polarization behavior indicates that no A'' transition gives appreciable contribution to the spectrum. This study reports also the aqueous spectrum that we have redrawn in Figure 1a. The authors quote four excitations, with = 37.5, 43.0, 45.2 and 50.0 x 103 cm-1, all of -* type.

While previous computations were restricted to vertical excitations, we have performed the first simulation of the complete spectrum of cytosine, using the Linear Vibronic Coupling (LVC) method.[12] In this method the full (electronic and nuclear) wave function is evaluated as a coordinate-dependent combination of the excited electronic wave functions at a reference geometry, normally the ground state equilibrium. The calculations require the derivatives of the excited state energy with respect to the ground state normal coordinates. The nuclear wave functions are expanded in the harmonic oscillator basis of the ground state. We used in the LVC model the four lowest excited electronic states (Table 1) and fourteen vibrational modes with several quanta on each of them. In addition, applying a new development to be published separately, the effect of non-adiabatic couplings was also included. The theoretical and experimental spectra are shown in Figure 1. The resolution of the simulated spectra was deliberately made low, to conform to the experimental spectrum. For details see the Supplement

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There is, however, a serious discrepancy with a REMPI study of laser-desorped, jet-cooled cytosine.[14] In the limited range studied, 31000-38000 cm-1, two vibronic regions were found and assigned to two tautomers! Region R1, 31800-32100 cm-1, should belong to the keto form and region R2, 36000-37600 cm-1, to the enol form. This interpretation would completely contradict our theoretical results: for the relevant transition I we have the range 36000-40000 cm-1 and accepting R1 would mean that our calculation is off by ~ 1 eV. This seems highly improbable: for four analogous -* excitations in pyrimidine, the differences are 0.3 to 0.4 eV[15] at the CCSD level and even less if triples are considered. The REMPI study on cytosine is supported by spectral hole-burning[14b] but the vibrational structure of R1 with splittings of 40-50 cm-1 is totally unexplained. It may be added that region R2, rather than R1, would be a reasonable candidate for the keto form in our results.

By contrast, two other experiments support our results. First, a recent study[16] measured the

resonance Raman spectra of cytosine around its 267 nm absorption (band I above). When scanning the exciting laser wavelengths from 290 nm to 244 nm, the spectra showed no change, "indicating that the Raman spectra are enhanced by a single electronic transition." At 244 nm a significant change in the excitation profile was observed, suggesting that "enhancement of the vibrations by the ~200 nm absorption band is becoming a factor". Thus, although the authors do not discuss explicitly the number of electronic transitions, their interpretation of the spectra is based on only two transitions, 267 and ~200 nm, corresponding to I and IV above.

Second, transition moments, an integral part of the calculations, can be compared with linear dichroism (LD) measurements on single crystals,[10,13] as well as on polycrystalline cytosine embedded in stretched polyvinyl alcohol sheets[9,17] (Table 2). The experimental values being by nature rather uncertain, we confirm ref.[17b] as opposed to ref.[17a] on band I. For band IV, theory makes clear selection between the alternatives in ref.[10] These LD measurements also give information about the spectrum interpretation discussed above: all experiments agree that the four absorptions involve transition moments in the plane of the molecule. In the theoretical results (Table 1), two of the four excitations are type A'' involving transition moments perpendicular to the molecular plane.

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N3

C2

N1

C6

C5

C4

O

NH2

-15o

32o

I

IV

Table 2. Transition Moment (µ) Directions in Cytosine[a]

Transition SingleCrystal[13]

SingleCrystal[10]

PVAFilm[17

a]

PVAFilm[17

b]

Theor.CCSD

Theor.CC3

I 14 (48) 6 9 25 32 34

IV --- 86 (-27) --- --- -15 -13

[a] angle in degrees between µ and the N1-C4 line, see Scheme 1.

PVA - Polyvinylalcohol.

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50

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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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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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The population of various tautomers in the gas phase is quite uncertain. There is general agreement about the dominance of the amino-hydroxy form (2), but theory also predicts a relative free energy of only G ≤ 1 kcal/mol for the amino-oxo (1) and even the imino-oxo form (3a). For both of the latter, this implies relative abundances of up to 20%. Spectroscopic studies do „see” these isomers but with smaller abundance.