Abstract— The total energy of intermolecular hydrogen bonds in 17α-hydroxyprogesterone crystal (17HP) estimated on the basis of the DFT/B3LYP calculations is significantly higher than that in progesterone crystal.

I. INTRODUCTION AND BACKGROUND Absorption bands observed in the vibrational spectra of

molecular crystals in the terahertz (THz) frequency range are determined both by the molecule structure itself and by the structure of the corresponding crystal. Previously we have shown that progesterone and 17HP molecular crystals have several intense vibrational features in the THz range [1]. Upon cooling, different temperature dynamics of the THz and Raman band positions was observed: in the progesterone crystals the most of the bands were shifted to lower frequencies upon cooling and in the 17HP absorption and Raman spectra the band positions were less sensitive to temperature variation. It was assumed that the temperature behavior depends on the ability of a molecule to form intermolecular hydrogen bonds, but the parameters of such behavior were not evaluated so far.

The aim of this work is to study intermolecular interactions in the molecular crystals of progesterone and 17HP.

II. RESULTS Analysis of the electronic density distribution function

ρ(r) in the crystals of steroid hormones has been carried out using the Bader’s method on the base of DFT/B3LYP calculations in the 6-31G(d) Gaussian-type basis set [2]. This method strictly describes the criterion of existence of the interatomic binding interaction; namely: the presence of the bond critical point (CP) of the (3, -1) type and the presence of bond path between the interacting atoms is the necessary and sufficient condition of existence of the chemical bond (interatomic binding interaction) independently of the bond nature. An important bond characteristic in the Bader theory terms is the value and sign of the electron density Laplacian

2 ( )ρ∇ r in the bond critical point. The value of the Laplacian 2 ( )ρ∇ r in the CP is a measure of electron density

concentration in the interatomic space. It is important that the ρ(r) and 2 ( )ρ∇ r values are experimentally verifiable by the precision X-ray diffraction analysis. Electron density analysis at the QTAIM level allows to detect some very weak hydrogen bonds and Van der Waals contacts (e.g. CH···O and H···H) which are characterized by extremely low ρ(r) values (at the critical point) measured experimentally by the high-precision X-ray diffraction analysis. An important advantage

of the AIM theory is the ability to estimate the energy of intra- and intermolecular interactions on the basis of Espinosa correlation scheme. This relationship links the energy of interaction with the potential energy density ν(r) in the corresponding critical point.

As it is known from the X-ray diffraction data the elementary cell of each investigated hormone consists of four molecules. The molecules are packed in the cell in such a way that each of them cooperates with all surrounded species in this unit cell. For analysis of the electronic density distribution we used the additive scheme of hormones crystal considering six dimer couples. The analysis of intermolecular О···Н bonds by the value of electronic energy density and by the sign of the Laplacian at the critical points for all dimers provides us the chance to attribute these contacts to the closed-shell interactions.

Among all found intermolecular bonds, a strong hydrogen О···Н bond in one of the 17HP dimers deserves our special attention. For this bond, the topological parameters of electronic density in a critical point were defined and the energy of internuclear interaction was evaluated on the basis of Espinosa’s correlation dependence. The 3O · HO17 hydrogen bond energy is equal to 7.12 kcal/mol. In addition to strong hydrogen bonds in the 17HP crystal, there are several O · H hydrogen bonds with the energy ranging from 0.06 to 1.92 kcal/mol, as well as H · H and C· H bonds that give an additional contribution to the stabilization of tetramers. The total energy of all intermolecular bonds is equal to 19.78 kcal/mol, which is significantly higher than the energy of the crystal packing of progesterone (9.67 kcal/mol). We suppose that this fact causes the absence of temperature-induced shifts in the IR absorption and Raman band positions in the THz region in 17α-hydroxyprogesterone upon cooling the crystal.

This work is supported by the Russian Foundation for Basic Research under grant № 13-02-01364.

REFERENCES [1] I. N. Smirnova, D. A. Sapozhnikov, A.V. Kargovsky, V. A. Volodin, O. P. Cherkasova, R.Bocquet, A.P.Shkurinov, “Lowest-lying vibrational signatures in corticosteroids studied by terahertz time-domain and Raman spectroscopies”, Vibrational Spectroscopy, 2012, vol.62, pp. 238-247. [2] G. V Baryshnikov, L. I. Tkachenko, V. A. Minaeva, B. F Minaev, O. P. Cherkasova, “The Bader theory analysis of intermolecular interactions in the crystal packings of sexual hormones, progesterone, 17α-hydroxyprogesterone, testosterone”, Vestnik Cherkassy University. Series: Chem. Sci., 2013, N 14(267), pp. 124-132.

O. P. Cherkasovaa, B. F. Minaevb, G. V. Baryshnikovb, L. I. Tkachenkob, V. A. Minaevab, I. N. Smirnovac, D. A. Sapozhnikovd, A.V. Kargovskyd, A. P. Shkurinovd

aInstitute of Laser Physics SB RAS, Novosibirsk, 630090 Russia bBogdan Khmelnitskij National University, Cherkassy, 18031Ukraine

cInstitute on Laser and Information Technologies of RAS, Troitsk, 142092 Russia dLomonosov Moscow State University, Moscow, 119991, Russia

Analysis of intermolecular interactions in progesterone and 17α-hydroxyprogesterone crystals

978-1-4673-4717-4/13/$31.00 ©2013 IEEE