Olga Dmitrenko

Institute of Surface Chemistry, National Academy of Sciences of Ukraine,

252022 Kiev, Ukraine

Wolfgang Reischl

Institute of Organic Chemistry, University of Vienna, A-1090 Vienna, Austria

James T. Vivian and John H. Frederick

Department of Chemistry, University of Nevada, Reno, NV 89557, USA

Abstract. Ground and excited states properties of previtamin D individual conformers are examined by use of the MMX (PCMODEL) empirical force field, and AM1 and QCFF/pi semi-empirical calculations. Ground state geometries obtained by these methods indicate a highly twisted triene system with similar degrees of non-planarityfor all conformers. The results for origin transitions support the suggestion that cZc conformers absorb at longer wavelength than tZc ones, thereby contributing to the understanding of wavelength dependence of previtamin D photochemistry.

Keywords. Previtamin D conformers, ground and excited states, force-field calculations,

AM1 conformational analysis, QCFF/PI calculations, absorption properties of conformers


The photochemical reaction of previtamin D formation from the steroidal diene precursor, provitamin D (7-dehydrocholesterol, Scheme 1), occurs in mammal skin and is the key step in the biogenesis of vitamin D [1]. The mechanisms of the photoreactions involved in previtamin D photosynthesis are still the subject of intensive investigations [2,3].


Reaction scheme of previtamin D photosynthesis (In vivo the side-reactions, cis-trans isomerization into tachysterol and irreversable photoconversions into toxisterols, are inefficient).

One of the open questions in previtamin D photochemistry is its wavelength dependence [3-5]. To gain a better understanding of this dependence, a detailed knowledge of the ground and excited states of the various conformers of this flexible steroid molecule is necessary. It has been suggested [3 and references therein] that the origin of the sudden change of quantum yields of previtamin D photoconversions at the red edge of the absorption band can be attributed to the selective excitation of ground state conformers that differ in their electronic absorption characteristics. Up to now little is known about the conformational population of previtamin D and, moreover, about the absorption properties of its individual conformers [3].

Here we will examine the previtamin D ground state conformations and the associated transitions to the lowest "bright" singlet excited state. The aim of this work is to calculate the absorption properties of previtamin D conformations and to show how they might contribute to the wavelength dependence of the photoreaction.

2. Computational details

For the ground-state conformational analysis we use the MMX force field from PCMODEL [6] and AM1 semi-empirical calculations [7]. In all the previtamin D structures, the hydrocarbon side chain has been substituted by a methyl group for simplicity. The first singlet excited states of 3-desoxy-previtamin D conformers(1) have been studied by the QCFF/pi program [8] developed by A.Warshel and M.Karplus for the calculation of the ground and excited states of large conjugated molecules. Like MMX, QCFF/pi is based on the formal s -- p separability: the F-potential surface is represented by empirical potential functions whereas B-electrons are treated by a semiempirical approach (Pariser-Parr-Pople type). In QCFF/pi, only singly excited B-electron configurations are included in the CI matrix. A number of studies (e.g. on stilbenes [9]) indicate that QCFF/pi computations are suitable for cases of large conformational changes, thereby supporting our choice for modeling the steroid trienes which are highly conformationally flexible and strongly distorted by steric interactions. The starting geometries of 3-desoxy-previtamin D conformers have been taken from the previous MMX optimizations of previtamin D by use of the default (charge-charge) calculation scheme of intramolecular electrostatic interactions [10].

3. Results and discussion

The detailed molecular-mechanics-based conformational search on previtamin D molecule and its analogs have been presented earlier in [10]. The results obtained there support the prognostic quality of MMX conformational analysis. However our recent computational studies [11] motivated by ultrafast studies of Fuss et al. [12] have revealed the serious problem in modeling a highly flexible molecule possessing a polar OH-group, namely, that the relative stabilities of different conformers are very sensitive to the modeling approach and, in particular, to the intramolecular interactions calculation scheme [11].

In contrast to the relative stabilities, the different previtamin D conformations themselves are somewhat reproducible using different computational approaches as is demonstrated in Table 1. For the description of individual conformers the following abbreviations are used: Z denotes the cis geometry of the C6=C7 double bound; letters c and t refer to the cis and trans geometries of C5-C6 and C7-C8 single bonds respectively; (-) or (+) indicates the sign of these torsion angles according to the rules of Klyne and Prelog [13].

Table 1. Selected torsion angles of previtamin D ground state conformers optimized by MMX- and AM1 semi-empirics.






































































The occurrence of conformers with large values of these torsion angles (independently derived from the different calculation approaches) allows us to conclude that these highly twisted non-planar structures are realistic and contribute significantly to the conformer population. This justifies their use as input data for UV spectra calculations. We believe that all twelve conformations found in our earlier work [10] contribute to UV absorption, thereby accounting for the absence of any structure in the absorption spectrum of previtamin D (see Figure) even at low temperature[4,5]












UV absorption spectrum of previtamin D

Since the QCFF/pi program does not provide parameters for a hydroxyl group, the 3b-OH group in previtamin D was replaced by a hydrogen atom.

We used the MMX derived previtamin D geometries as input structures for the QCFF/pi calculations and due to the half-chair -- half-chair interconversion of the A-ring, again two sets of conformers have been obtained. In one set of six conformers, the 3ß-hydrogen is in equatorial orientation; whereas, in the other six conformers the 3ß-hydrogen is found in an axial orientation. Selected data for the ground- and first allowed excited state geometries of 3-desoxy-previtamin D conformers are given in Table 2. Comparison of the ground state torsion angles obtained after minimization by QCFF/pi with initial (MMX optimized) angles reveals no significant changes (Table 1 and Table 2). Thus, re-optimization by QCFF/pi does not cause any marked changes in the ground state geometries of the steroid triene system.

Some trends are observed for the geometry changes in the conformers upon excitation. All the optimized excited singlet conformers possess more planar torsion angles about the single bonds and significantly distorted planarity (up to 45deg) about the central doble bond, C5-C6=C7-C8.

Table 2. Changes in the torsion angles of triene system of desoxy-previtamin D conformers upon excitation. The ground state values are given in parentheses.

Conformer C10=C5-C6=C7 C5-C6=C7-C8 C6=C7-C8=C9

3ß-H equatorial

(-)cZ(-)c -33 (-68) -42 (-10) -19 (-43)
(+)cZ(+)c 23 (52) 35 (7) 16 (37)
(-)tZ(+)c -150 (-126) 40 (9) 16 (39)
(+)tZ(-)c 173 (151) -45 (-14) -21 (-45)
(+)tZ(+)t 161 (133) -43 (-11) 144 (121)
(-)cZ(+)t -24 (-50) -37 (-6) 150 (129)

3ß-H axial

(-)cZ(-)c -30 (-62) -41 (-12) -17 (-39)
(+)cZ(+)c 26 (57) 36 (7) 18 (40)
(-)tZ(+)c -170 (-147) 42 (11) 26 (52)
(+)tZ(-)c 145 (121) -43 (-11) -14 (-36)
(+)tZ(+)t 161 (136) -41 (-9) 152 (130)
(-)cZ(+)t -21 (-46) -37 (-6) 151 (130)

The characteristic data upon excitation of the previtamin D conformers are summarized in Table 3. Vertical transitions (which reflect the absorption maximum) do not appear to be specifically dependent on the triene geometry; whereas, the values of the oscillator strength clearly suggest that conformers with at least one s-trans bond possess a stronger absorption [1]. The results for the origin transitions clearly show that cZc conformations absorb at longer wavelength than those containing at least one s-trans bond. This is in agreement with earlier predictions suggested in numerous studies (see, for example [1]) as well as with the recent measurements of Fuss and Lochbrunner [5]. They have measured the low temperature UV spectrum of cZc conformer just formed from its precursor, provitamin D, and compared it with the low temperature spectrum for equilibrated previtamin D. At wavelengths longer than 310 nm, the absorption of cZc conformer was far larger than the absorption of tZc [5].

Table 3. Electronic transitions of desoxy-previtamin D conformers*.

Conformer Excitation energy, cm-1 (wavelength, nm) Oscillator strength wavelength 0-0, nm

3ß-H equatorial

(-)cZ(-)c 40343.1 (248) 0.35 314
(+)cZ(+)c 37134.0 (269) 0.3 325
(-)tZ(+)c 38857.1 (257) 0.39 307
(+)tZ(-)c 37310.9 (268) 0.58 311
(+)tZ(+)t 42074.7 (238) 0.73 283
(-)cZ(+)t 39213.9 (255) 0.45 301

3ß-H axial

(-)cZ(-)c 38626.6 (259) 0.35 318
(+)cZ(+)c 38274.0 (261) 0.3 323
(-)tZ(+)c 38795.9 (258) 0.52 304
(+)tZ(-)c 38956.9 (257) 0.38 307
(+)tZ(+)t 40637.7 (246) 0.85 284
(-)cZ(+)t 38571.2 (259) 0.47 304

*In the results presented, only singly excited B-electron configurations were included in the CI matrix. Thus, just the allowed 1B2 singlet excited state mostly contributing to the UV absorption is under consideration [14].

Thus, one may attribute the different photochemical behaviour at the red edge of previtamin D absorption band to the selective excitation of cZc conformers. This also may be one of the reasons for the dramatic increase in the efficiency of toxisterols formation observed by Terenetskaya et al. [15] upon long-wavelength photolysis of provitamin D. However, Fuss and Lochbrunner have recently postulated [5] that the dominant origin of wavelength dependence in previtamin D photochemistry may be caused by an isomerization process (double bond isomerization) on the excited state surface which possesses an energy barrier. As the excitation wavelength is shortened this process compete with other barrierless reactions, thereby altering all the quantum yields[5].


Our results, obtained using a variety of different computational methods, indicate a great predominance of non-planar geometries for the individual previtamin D conformers than had been found earlier by MMP2 computational studies alone [16]. Thus, the highly twisted triene moiety of previtamin D molecule (which plays a central role in its structural and photophysical properties) must be properly accounted for when extrapolating from the properties of simpler model trienes.

In addition our results for the origin excitations support the earlier assumptions of Jacobs and Havinga [1], namely, that cZc conformers absorb at longer wavelengths than tZc ones. This means that it is important to consider both the excited state effects [5] and selective excitation of ground state conformations [3], when discussing the wavelength dependence of previtamin D photosynthesis. The present results are performed for gas-phase conformations and reflect a general tendency. For qualitative comparison with the experimental observations they require futher corrections for solvent effects. Moreover, for non-planar structures the s -- p separation is no longer strictly valid; thus, the results obtained here should be considered as a qualitative first approximation.

5. Acknowledgments

We are grateful to W. Fuss for valuable e-mail discussions. O.D. acknowledges financial support through the U.S. National Science Foundation (CHE-9419102 to J.H.F.) and a Fellowship from the President of Ukraine. Access to an SGI workstation was made possible by a grant of the Fonds zür Förderung der wissenschaftlichen Forschung (P09859-CHE, to W. Weissensteiner). Financial support from the NSF and Österreichische Nationalbank (Jubilaeumsfondsprojekt Nr.: 4865) are gratefully acknowledged.

6. References

1 H.J.C.Jacobs and E.Havinga, Adv. Photochem. 11 (1979) 305-373; A.W. Norman, "Vitamin D, The Calcium Homeostatic Steroid Hormone" Academic Press: New York, 1979
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3 H.J.C.Jacobs, Pure Appl.Chem.67 (1995) 63-70; A.M.Brouwer, J. Cornelisse, H.J.C.Jacobs,Tetrahedron 43 (1987) 435-438
4 W.G. Dauben, B.Disanyaka, D.J.H.Funhoff,B.E. Kohler, D.E. Schilke, B. Zhou, J.Am.Chem.Soc. 113 (1991) 8367-8374
5 W. Fuss and S. Lochbrunner, J.Photochem. Photobiol.A:Chem 105 (1997) 159-164
6 N.L.Allinger and H.L.Flanagan, J. Comput. Chem., 4 (1983), 399; G -MMX and PCMODEL (Serena Software, Bloomington, Indiana) for SGI Indigo 2.
7 M.J.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P. Stewart, J.Am.Chem.Soc. 107 (1985) 3902-3909
8 A.Warshel and M.Karplus, J.Am.Chem.Soc. 94 (1972) 5612-5625; Quantum Chemistry Program Exchange,Indiana University. Program No. 534
9 A.Warshel, J. Chem. Phys. 62 (1975) 214-221
10 O.Dmitrenko and W.Reischl, Monatsh. für Chemie 127 (1996) 445 -453;

O. G. Dmitrenko, I.P. Terenetskaya and W. Reisch, J.Photochem. Photobiol.A: Chem. 104 (1997) 113-117 ; O. Dmitrenko and W. Reischl, Res. Chem. Intermed. (1997) in press

11 O.G.Dmitrenko and W.Reischl, J.Mol.Struc.(Theochem), accepted for publication
12 W. Fuss, T. Hoffer, P. Hering, L.P. Kompa, S. Lochbrunner, T. Schikarski and

W.E. Schmid, J. Phys. Chem. 100 (1996) 921-927;

13 W.Klyne and V.Prelog, Exerientia 16 (1960) 521-530
14 T. Liljefors and N.L.Allinger, J.Am.Chem.Soc. 98 (1976) 2745-2749
15 I.P.Terenetskaya, S.I.Gundorov, V.I.Kravchenko, I.K.Berik, Sov.J.Quantum. Electron. 18 (1988) 1323-11328
16 W.G.Dauben and D.J.H.Funhoff, J.Org.Chem.53 (1988)5070-5075


1. QCFF/pi in the version used here is developed for conjugated hydrocarbons and, unfortunately, does not contain parameters for treatment of hydroxyl group in previtamin D molecule. Nevertheless, we do believe that the use of its desoxy- analog provides a good first approximation for the excitation energies.