- Email: [email protected]
Symmetry adapted cluster–configuration interaction calculation of the photoelectron spectra of famous biological active steroids
Journal of Molecular Structure 1076 (2014) 69–79
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Symmetry adapted cluster–configuration interaction calculation of the photoelectron spectra of famous biological active steroids Fatemeh Abyar, Hossein Farrokhpour ⇑ Chemistry Department, Isfahan University of Technology, Isfahan 84156-83111, Iran
g r a p h i c a l a b s t r a c t
h i g h l i g h t s Gas phase ionization energies of
important steroids were calculated. Population ratios of conformers of BWP
Intensity (arb.uni)
each steroid were calculated in the gas phase. Ten ionization energies were calculated for each steroid. The spectral bands of each steroid were assigned by NBO calculations. The calculated photoelectron spectra were in good agreement with the experiment.
14
13
12
11
10
9
8
Binding Energy (eV)
a r t i c l e
i n f o
Article history: Received 29 June 2014 Received in revised form 15 July 2014 Accepted 15 July 2014 Available online 22 July 2014 Keywords: Ionization energy Steroids Photoelectron spectroscopy SAC–CI NBO Cholesterol
a b s t r a c t The photoelectron spectra of some famous steroids, important in biology, were calculated in the gas phase. The selected steroids were 5a-androstane-3,11,17-trione, 4-androstane-3,11,17-trione, cortisol, cortisone, corticosterone, dexamethasone, estradiol and cholesterol. The calculations were performed employing symmetry-adapted cluster/configuration interaction (SAC–CI) method using the 6311++G(2df,pd) basis set. The population ratios of conformers of each steroid were calculated and used for simulating the photoelectron spectrum of steroid. It was found that more than one conformer contribute to the photoelectron spectra of some steroids. To confirm the calculated photoelectron spectra, they compared with their corresponding experimental spectra. There were no experimental gas phase HeAI photoelectron spectra for some of the steroids of this work in the literature and their calculated spectra can show a part of intrinsic characteristics of this molecules in the gas phase. The canonical molecular orbitals involved in the ionization of each steroid were calculated at the HF/6-311++g(d,p) level of theory. The spectral bands of each steroid were assigned by natural bonding orbital (NBO) calculations. Knowing the electronic structures of steroids helps us to understand their biological activities and find which sites of steroid become active when a modification is performing under a biological pathway. Ó 2014 Elsevier B.V. All rights reserved.
Introduction Generally, steroids are known as hormones in biology. Hormones are materials which are produced at one site in the body ⇑ Corresponding author. Tel.: +98 311 3913243; fax: +98 311 3912350. E-mail addresses: (H. Farrokhpour).
[email protected],
http://dx.doi.org/10.1016/j.molstruc.2014.07.040 0022-2860/Ó 2014 Elsevier B.V. All rights reserved.
[email protected]
of organism and acts at the other site. All steroid hormones are derived from cholesterol by a number of precise modifications to the cholesterol structure, with different series of modifications occurring in different pathways [1]. The main skeleton of molecular structure of steroid is composed of the ring system of three cyclohexanes and one cyclopentane in a fused ring system and different functional groups can be attached to this fused ring system [2] (see Scheme 1). The biological activities of steroids depend on
70
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
F
Scheme 1. Simple basic molecular structure of steroids considered in this work.
their structures [3–5] so that a little change in their molecular structures vary the number of populated conformers of steroid in the gas phase and yields dramatic changes of intensity and modes of action [6]. Change in the action of steroid has direct correlation with its electronic structure. Another important aspect of steroids which has direct correlation with their electronic structure is finding the region of steroid which can be attacked in biological pathways. One of the best methods to obtain information about the electronic structures of molecules is photoelectron spectroscopy. Among the considered steroids in this work, there are only the experimental gas phase HeAI photoelectron spectra for 5a-androstane-3,11,17-trione [7], corticosterone [8] and a thin film of cholesterol on hydroxypropionitrile solution running down a tungsten rod [9] in the literature. There are a limited number of theoretical works on the electronic structure of steroids in the literature which they use semi-empirical methods for calculating the ionization and molecular orbital energies of different series of steroids [7–15]. The semi-empirical methods used in this context are AM1, MNDO and HAM/3. The only ab initio calculation on the electronic structure of steroids is related to the work of Pasa-Tolic et al. [9]. which performed simple ab initio calculations on 5a-androstane steroid by self-consistent field (SCF) method using a very small basis set (STO-3G). It should be mentioned that the electronic correlations which are important in the energy order of molecular orbitals of each compound are absent in the computational methods used for the steroids in the literature. The selected steroids in this work are 5a-androstane-3,11,17-trione, 4-androstane-3,11,17-trione, cortisol, cortisone, corticosterone, dexamethasone, estradiol and cholesterol. One of the motivations for calculating the ionization energies of the steroids in this work is that the electronic structure of steroid is an important factor in determining its biological activities. Therefore, calculating the ionization energies of steroids and assigning their photoelectron spectra helps us to understand their electronic structures and find the most probable ionization sites in them relevant to their biological activities. The other motivation is that there is no report, experimentally and theoretically, on the gas phase ionization energies of some considered steroids in this work
Intensity (arb.uni)
E
D
C
B A
(nO(C=O); ring A)
(nO(C=O); ring C and D)
a nO(C=O); ring C and D (nO (C=O) ; ring D, C;πC=C) (nO (C=O) ; ring A; πC=C) πC=C
b 14
13
12
11
10
9
8
7
Binding Energy (eV) Fig. 2. (a) The experimental HeAI photoelectron spectrum of 5a-androstane3,11,17-trione [6] (black solid line) compared with its calculated photoelectron spectrum obtained using SAC–CI SD-R/6-311++G(2df,pd) level of theory (blue solid line). The calculated spectrum has been shifted as +0.8 eV (see ‘5a-Androstane3,11,17-trione’). (b) Red trace shows the simulated photoelectron spectrum of 4androstene-3,11,17-trione obtained at the same level of theory. Vertical lines show the energy position and intensity of the calculated ionization bands. The arrows in the figure show the assignment of the selected ionization bands. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
except for 5a-androstane-3,11,17-trione and corticosterone. Some of the steroids have a lot of conformers in the gas phase and using the theoretical calculations with the aid of the experimental photoelectron spectrum, it is possible to understand which conformers have dominant contributions in the spectrum of steroid and are responsible for the biological activity of steroid. The gas phase experimental and theoretical information on the fundamental properties of biological molecules are very important in understanding many biological phenomena and providing insight into the physicochemical origin of the properties of biological molecules. One of the most important physicochemical properties of biomolecules is their ionization potentials which are useful quantum mechanical diagnostics for oxidative potentials of these
Fig. 1. The molecular structures of (a) 5a-androstane-3,11,17-trione and (b) 4-androstene-3,11,17-trione.
71
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Table 1 The ionization energies of steroids, calculated at the SAC–CI-SD-R level of theory using 6-311++G(2df,pd) basis set. The superscript roman letters show the conformer number. Compound 4-Androstene-3,11,17-trione 5a-Andestron-3.11.17-trion Cortisol Cortisone
Corticosterone
Dexamethasone Estradiol Cholesterol a b
I1 (eV) b
7.987(0.906) 8.787a 7.930(0.912) 8.73a 8.516(0.930) 8.981a 8.543(0.910)I 9.008a,I 8.553(0.913)II 9.018a,II 8.525(0.929)I 8.990a,I 8.562(0.928)II 9.027a,II 8.806(0.931) 9.271a 6.622(0.927) 7.197a 7.936(0.94)
I2
I3
I4
I5
8.171(0.895) 8.971 8.301(0.911) 9.101 8.64(0.890) 9.105 8.638(0.915) 9.103 8.654(0.913) 9.119 8.619(0.891) 9.084 8.645(0.891) 9.11 8.937(0.877) 9.402 7.462(0.924) 8.037 8.804(0.93)
8.383(0.920) 9.183 8.713(0.904) 9.513 9.221(0.927) 9.686 8.923(0.911) 9.388 8.912(0.912) 9.377 9.192(0.926) 9.657 9.256(0.926) 9.721 9.260(0.933) 9.725 8.316(0.923) 8.891 9.228(0.93)
8.824(0.903) 9.624 9.341(0.919) 10.141 9.632(0.930) 10.097 9.591(0.922) 10.056 9.784(0.920) 10.249 9.679(0.923) 10.144 9.651(0.920) 10.116 9.479(0.930) 9.944 8.611(0.920) 9.186 9.731(0.937)
9.533(0.917) 10.333 9.798(0.915) 10.598 9.816(0.926) 10.281 10.074(0.927) 10.539 10.080(0.928) 10.545 9.827(0.923) 10.292 9.823(0.926) 10.288 10.235(0.933) 10.7 8.932(0.921) 9.507 9.999(0.938)
Shifted calculated ionization energies. The numbers in parenthesis are the intensity of ionization bands.
molecules. For example, when a photoionization or photoabsorption process occurs in a biological system such as living cells, it may cause certain photobiological effects on the system such as damage, cell death, or mutation. Therefore, knowing the values of ionization energies of biomolecules is important for unraveling the mechanism of protein, DNA, and cell damage due to photoionization. To the best of author knowledge, there is no high level ab initio quantum chemical calculations on the electronic structure for molecules as large as the steroids (fascinating compounds) in the literature. In addition, there is no information about the ionization energies of steroids in the NIST Chemistry Webbook [16]. It was found that a high level ab initio method such as SAC–CI is a proper method for calculating the valence and core ionization of molecules [17–26]. In this work, the ionization energies of the considered steroids are calculated employing SAC–CI method and their calculated photoelectron spectra assigned.
Methodology The SAC–CI-SD-R method which uses the single and double excitation operators along with the 6-311++G(2df,pd) basis set was employed for calculating the ionization energies. This method uses all single excitation operators and the double excitation operators are included when their second-order contribution in energy are larger than a given threshold (k = 10 6; level three) in the SAC calculations to obtain the energy and wave function of the ground state of neutral molecule [27–29]. For unlinked operators, the products of linked operators whose SDCI coefficients of higher than 5 10 3 were also used in the SAC calculations. Optimized geometries and Boltzmann population ratios (BPR) of conformers of each molecule were calculated at the B3LYP/6-31+G(d) level of theory. The calculated BPR of the conformers of each steroid, the calculated ionization cross sections and the ionization energies of each conformer were used to simulate the photoelectron spectrum of each steroid. The ionization cross sections were calculated using the monopole approximation [30], which allows the correct estimation of the relative intensities of ionization bands. For calculating the monopole intensities, the correlated SAC wave function of the ground electronic state of neutral molecule and SAC–CI SD-R wave functions of the related ionic electronic states were used. Furthermore, NBO calculations using Gaussian NBO (version 5)
[31] were performed at the Hartree–Fock (HF)/6-311++G(d,p) level of theory to calculate the canonical and natural bonding molecular orbitals at the ground electronic state for the spectral band assignment. All of the calculations were performed using the Gaussian Quantum Chemistry Package [32]. Result and discussion As mentioned before, there are different conformers for each steroid which some of them can be populated in the gas phase. The molecular structures of conformers of the steroids in this work have been taken form pubchem website [33]. There is complete information about the different conformers of steroids in this website. Figs. S1–S5 (supplementary material) show the molecular structures of conformers of corticosterone, cortisol, cortisone, dexamethasone, and cholesterol taken from pubchem website, respectively. The molecular structures of conformers of each steroid were optimized at the B3LYP/6-31+G(d) level of theory and then frequency calculation were performed on the optimized structures, at the same level of theory, to obtain the population ratio of conformers in the gas phase in the temperature range of 160 to 180°C used for evaporating of steroids, reported in the literature [9]. The population ratios of conformers of the steroids in this work have also been reported in Figs. S1–S5. As seen in Fig. S5 cholesterol has eight conformers and only one of them is populated in the gas phase. Similarly, corticosterone and cortisone have only two populated conformers in the gas phase (Figs. S1 and S3). Cortisol and dexamethasone have only one populated conformer in the gas phase. Pubchem website proposes only one conformer for 5a-androstane-3,11,17-trione, 4-androstane-3,11,17-trione and estradiol. In the next sections, the photoelectron spectrum of each steroid and its assignment are explained, separately. 5a-Androstane-3,11,17-trione The structure of this steroid has been shown in Fig. 1. There is only one experimental photoelectron spectrum for 5a-androstane-3,11,17-trione in the literature [6]. As seen in Fig. 1, at the first glance, there are three oxygen atoms in this steroid containing lone electron pairs and three pC@O (p electrons of C@O bond) which can be considered as ionization sites in this steroid. It is important to know the ionization energy
72
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Fig. 3. The canonical molecular orbitals of (a) 5a-androstane-3,11,17-trione and (b) 4-androstene-3,11,17-trione.
order of these sites. Fig. 2 compares the calculated photoelectron spectrum of 5a-androstane-3,11,17-trione (blue spectrum in Fig. 2) with its experimental photoelectron spectrum (black spectrum in Fig. 2) [7]. It can be seen that the simulated spectrum of 5a-androstane3,11,17-trione can describe the three feature A, B and C of the experimental spectrum well. Unfortunately, the resolution of the reported experimental spectrum is not enough to see the other calculated features in it. It seems that there is considerable background in the experimental spectrum for the binding energies higher than 10 eV. In this case, theoretical calculations are useful to distinguish the ionization bands in the region of the photoelectron spectrum which is not resolved. The simulated spectrum of this steroid has been shifted by +0.8 to higher binding energy for matching with the experimental spectrum. It should be mentioned that although, the value of energy shift is relatively large because of the size of molecule but, comparison of the shifted spectrum
with the experimental spectrum confirms that the SAC–CI method can relatively well predict the relative energy positions of the ionization bands. Table 1 reports the calculated ionization energies of 5a-androstane-3,11,17-trione and the corresponding ionization energies considering +0.8 eV energy shift. Comparison of the experimental spectrum with the theoretical spectrum shows that features A, B and C of the experimental spectrum are composed of one ionization band, separately. Table S1 tabulated the main configuration of the ionic states and the dominant natural bonding orbital contributions in the canonical orbitals involved in the ionization for 5a-androstane3,11,17-trione. The first ionization band of 5a-androstane3,11,17-trione (feature A) is related to the ionization from HOMO with nonbonding character due to the lone electron pairs of oxygen of carbonyl bonds of rings C and D (Table S1; Fig. 2). The second ionization originates from HOMO-1 with nonbonding character but, because of the lone electron pairs of oxygen atom of carbonyl
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
conformer I (%25.3)
73
conformer I (%59)
conformer II (%74)
conformer II (%41)
(b)
(a)
(c) Fig. 4. The molecular structures of (a) the conformers of corticosterone, (b) the conformers of cortisone and (c) cortisol.
group of ring A. It is seen that the ionization energy of the lone electron pairs of oxygen atom of ring A is higher than that of the oxygen atoms of rings C and D. The assignment of the third ionization band, due to the ionization from HOMO-2, is mainly related to the nonbonding electrons of oxygen atom of ring D. The forth and fifth ionization bands are related to the ionization from HOMO-3 and; HOMO-4 and HOMO-5 orbitals, respectively. These molecular orbital have mainly r character due to CAC and CAH bonds (see Table S1). It is evident from Table S1 that the Koopmans’ theorem [34] is nearly valid for the considered assigned ionization bands of this steroid because the energy order of molecular orbitals of this steroid for ionization is HOMO > HOMO-1 > HOMO-2 > HOMO3 > HOMO-4. The main configuration of the wave functions of the first, second, third and fourth ionization bands of 5a-androstane3,11,17-trione are single HF ionized determinants (Table S1) which
shows that the electron correlations in these ionic states are not intense. The shape of the canonical molecular orbitals of 5a-androstane-3,11,17-trione have been shown in Fig. 3. The assignment of the photoelectron spectrum of this steroid and the shape of the HOMO of this steroid (Fig. 3) shows that the most probable reactive regions of this steroid are rings C and D (especially oxygen atoms) which are important in the biological activity of this steroid. 4-Androstane-3,11,17-trione (adrenosterone) Adrenosterone is a prohormone and its conversion hormone is known as 11-ketotestosterone, which is quite an interesting hormone, being a mild androgen in humans and a sex steroid in fish. 11-oxo is a non-aromatizing analog of testosterone, which causes dry lean gains and fat loss, along with an increased sexual desire
74
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
5a-androstane-3,11,17-trione have been shown in Fig. 3. Therefore, the most probable reactive region of this steroid is rings C and D (oxygen atoms) but, there is also some reactivity in ring A due to C@C bond. The wave function of the second ionic state is a linear combination of HOMO and HOMO-2 (major contribution). HOMO-2 is mostly related to the lone electron pairs of oxygen atom connected to ring A. Similar to the first ionization band, the ionization of the steroid from the p electrons of C@C bond can also take place in the second ionization band. It should be mentioned that the ionization probability of this steroid from the lone electron pairs of oxygen atom in the first and second ionization bands is about six times higher than the ionization from C@C bond. The wavefunction of the third ionic state is a linear combination of three HF ionized determinant related to HOMO (major contribution), HOMO-1 and HOMO-2. Table S2 shows that the ionization of steroid from the p electrons of C@C bond mainly occurs in the third ionization band. The ionization probability from HOMO is about five times higher than that of HOMO-1 and HOMO-2 in the third ionization band. Finally, it should be mentioned that the ionization of the p electrons of C@O bonds of 4-androstane-3,11,17trione and 5a- androstane-3,11,17-trione does not take place below 11 eV.
F E D C
Intensity (arb.uni)
B
A
BWP total
(nO(O-H) ; ring D) (nO(C=O) ; ring A)
π conformer 2
conformer 1
Corticosterone 14
13
12
11
10
9
8
Binding Energy (eV) Fig. 5. The experimental HeAI photoelectron spectrum of corticosterone [9] (black solid line) compared with its Boltzmann weighted photoelectron (BWP) spectrum (green trace) calculated at the SAC–CI SD-R level of theory. Vertical lines show the energy positions of the calculated ionization bands. Traces red and blue show the calculated photoelectron spectra of conformers 1 and 2 of corticosterone, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
[35]. The difference between 4-androstane-3,11,17-trione and 5aandrostane-3,11,17-trione is related to the presence of the unsaturated C@C bond in the 4-androstane-3,11,17-trione. As shown in Fig. 2, The shape of the calculated photoelectron spectrum of 4-androstane-3,11,17-trione (red spectrum) is different from 5a-androstane-3,11,17-trione although, there are similarity between their molecular structures. It is seen that the first, second and third ionization bands of this steroid form one feature in the calculated spectrum. There is no experimental photoelectron spectrum for this steroid in the literature for comparing with the theoretical spectrum. Table S2 tabulated the main configurations of the ionic wave functions (obtained from SAC–CI calculations) and the dominant natural bonding orbital contributions in the canonical orbitals involved in the ionization for 4-androstane3,11,17-trione. Comparison of Table S2 with S1 shows that the amount of the electronic correlations in 4-androstane-3,11,17-trione is higher than that in 5a-androstane-3,11,17-trione because the wave function of the first, second and third ionic states are linear combination of two or three HF single ionized determinants. Therefore, the Koopmans’ theorem is not valid for 4-androstane3,11,17-trione. The first ionization band of 4-androstane-3,11,17-trione is related to the ionization from HOMO and HOMO-1 (major contribution) with different contributions (Table S2). Therefore, the first ionization of this steroid takes place from HOMO-1 unlike to what was seen for 5a-androstane-3,11,17-trione. HOMO has p character due to the p electrons of C@C bond of ring A and HOMO-1 is mostly related to the lone electron pairs of oxygen atoms of rings A, D and C (especially rings C and D). Therefore, there is probability of the ionization of this steroid from the C@C bond of ring A in the first ionization band. The shape of the canonical molecular orbitals of
Corticosterone is an adrenocortical steroid that has modest but significant activities as a mineralocorticoid and a glucocorticoid. It has multiple effects on memory. The main effects are seen through the impact of stress on emotional memories as well as long term memory (LTM) [36]. There are three conformers for this steroid (see Fig. S1) which two of them are populated in the gas phase based on the thermochemistry calculations (Fig. 4). The difference between two populated conformers in gas phase is related to the rotation of a-hydroxy carbonyl group connected to ring D. The population ratio of conformer II is higher than that of conformer I (Fig. 4). Fig. 5 shows the calculated spectra of the conformers of corticosterone along with its BWP spectrum. The BWP spectrum has been shifted as +0.465 eV for matching its first feature with the first peak of the experimental spectrum (feature A). The agreement between the BWP spectrum and the experimental spectrum [9] is well. The relative energy positions of the calculated ionization bands of conformer I are nearly similar to that of conformer II for the binding energies below 11 eV. The assignment of the experimental photoelectron spectrum of corticosterone is performed based on the SAC–CI and NBO results of conformer II (Table S3) because of its higher population. Feature A of the experimental spectrum composed from the first ionization bands of conformers I and II. The first ionization band of conformer II originate from HOMO with p character due to the C@C bond of ring A. It is seen that the assignment of the first ionization band of this steroid is different to what was seen for 4-androstane3,11,17-trione (ionization of lone electron pairs of oxygen atom of rings D and C). The second ionization band is related to the nonbonding electrons of oxygen atom of ring A (HOMO-1). Therefore, the most probable reactive region of this steroid is the C@C bond of ring A. The third ionization band is related to HOMO-2 which has mainly r character although, there are some contributions from the lone electron pairs of the oxygen atoms of ring C and ahydroxy carbonyl group of ring D (Table S3). Similar assignment is valid for the fourth ionization band (ionization from HOMO-3). It is interesting to notice that the ionization of this steroid from the oxygen sites does not take place in the third and fourth ionization bands of this steroid unlike to what was seen for the previous steroids. The sixth ionization band is related to the ionization of the lone electron pairs of OH group of a-hydroxy carbonyl group of ring D and corresponds to feature D in the experimental spec-
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
75
Fig. 6. The canonical molecular orbitals of (a) corticosterone, (b) cortisone and (c) cortisol.
trum. It is evident from Table S3 that the Koopmans’ theorem is nearly valid for the first, second and third ionization bands of this steroid. The wave function of the fourth and fifth ionization bands are a linear combination of HOMO-3 and HOMO-4 with different contributions which shows that the electronic correlations have been increased in these ionic states. The assignment of the ionization bands of conformer I of corticosterone and the shape of its canonical molecular orbitals is similar to conformer II. Fig. 6a shows the canonical molecular orbitals of conformer II of corticosterone. Cortisone Cortisone is one of the main hormones released by the adrenal gland in response to stress. In addition, it is used to treat a variety of aliments and can be administered intravenously, orally, intraarticularly or transcutaneously. Similar to corticosterone, cortisone has three conformers (see Fig. S2) and only two of them are populated in the gas phase (Fig. 4b). The difference between cortisone and cortisol is related to the conversion of C@O bond to CAOH
bond in ring C. Fig. 7 shows the calculated photoelectron spectra of two conformers of cortisone. Comparison of Table S4 with S3 shows that the amount of electron correlation in the first, second and third ionic states of cortisone are higher than that for cortisol because the wave functions of these ionic states are a linear combination of single ionized HF determinants. The wave function of the first ionic state of cortisone is a linear combination of two single ionized determinants related to HOMO and HOMO-1 with the contributions comparable with each other (see Table S4). This means that the ionization from HOMO and HOMO-1 takes place in the first ionization bands with the nearly same probability. HOMO is mostly localized on the C@C bond of ring A and HOMO-1 is mostly due to the lone electron pairs of oxygen atom of ring A. Therefore, the most probable region for the biological activity of this steroid is ring A (oxygen atom and C@C bond) while, the first ionization band of corticosterone is only related to the C@C bond of ring A. The second ionization band is a linear combination of three ionized HF determinants related to HOMO, HOMO-1 and HOMO-2. Similar to HOMO-1, HOMO-2 has been localized more on the oxygen atoms of rings A and C com-
76
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
(nO(C=O) ; ring A)
of ring A. Therefore, it is reasonable to shift the calculated spectrum of cortisol by +0.465 eV to the higher binding energy although there is no experimental spectrum for this steroid in the literature. The first feature in the calculated spectrum contains of two ionization bands. The assignment of the second ionization bands of cortisol is same as that of corticosterone (Table S5). Therefore, the first and second ionization takes place in the ring A of steroid and the most probable reactive region of this steroid is ring A (especially C@C bond). Fig. 6c shows that there is similarity between the canonical molecular orbitals of cortisol and corticosterone. It is evident from Table S5 that the amount of the electronic correlation in cortisol is small compared to corticosterone and cortisone and the Koopmans’ theorem is completely valid for it. Fig. 6c shows that HOMO-2, HOMO-3 and HOMO-4 are completely distributed on the molecule and they are not localized on the special region of molecule. HOMO-3 is slightly localized on the a-hydroxy carbonyl group.
πC=C
Intensity (arb.uni)
d
BWP spectrum
c
b
Dexamethasone
conformer 2
(nO(C=O) ; ring D)
(nO(C=O) ; ring A ,C; π
a conformer 1 14
13
12
11
10
9
8
7
Binding Energy (eV) Fig. 7. The calculated photoelectron spectra of conformers of cortisone (spectrum a and b) along with their Boltzmann-weighted photoelectron spectrum (labeled with ‘‘BWP’’ in the figure) obtained at the SAC–CI SD-R level of theory. Trace d shows the calculated photoelectron spectrum of cortisol. The arrows in the figure show the assignment of the selected ionization bands.
pared to other regions of molecule. Fig. 6b shows that the localization of the HOMO-2 on the oxygen atom of ring A in cortisone is higher than corticosterone. Table S4 shows that the ionization probability of steroid from C@C bond in the second ionization band is more than the first one because the contribution of the single ionized HF determinant relevant to HOMO is higher than the other determinants in the wave function of the second ionic state. The wavefunction of the third ionization band is mostly related to HOMO-2 but there is some contribution from HOMO. Therefore, there is also probability of ionization of p electrons of C@C bond in this ionization band. It is seen that the first, second and third ionization bands have similar assignment. The wave function of the fourth ionization band is composed of only one single ionized HF determinant related to the ionization from HOMO-3. HOMO-3 is mostly related to the oxygen of carbonyl of a-hydroxy carbonyl group connected to ring D. The difference between the HOMO-3 of cortisone and corticosterone is related to the localization of orbital on ring A and B (see Fig. 6). Cortisol Cortisol is a hormone which is released in response to stress and a low level of blood glucocorticoid. It has three conformers (see Fig. S3) which only one of them is the most stable conformer in the gas phase (Fig. 4c). Fig. 7 shows the calculated photoelectron spectrum of cortisol and its ionization energies have been reported in Table 1. There is no experimental photoelectron spectrum for cortisol in the literature for comparing with the theory. Therefore, it is worthwhile to have information about its photoelectron spectrum from the theoretical calculations. As shown in Table S5, similar to corticosterone, the first ionization of this steroid is due to the ionization of HOMO related to the p electrons of C@C bond
Dexamethasone has anti-inflammatory and immunosuppressant effects and it is on the World Health Organizations (WHO) list of Essential Medicines (Fig. 8). Dexamethasone have two conformers (see Fig. S4) and only one of them is populated in the gas phase (Fig. 8a). There is no theoretical and experimental report on the gas phase photoelectron spectrum of dexamethasone in the literature. The calculated photoelectron spectrum of dexamethasone has been shown in Fig. 9 (spectrum a). As seen in Table S6, the wavefunctions of the ionic states of dexamethasone are composed of single ionized HF determinants. Similar to corticosterone, the first ionization band of dexamethasone is related to the ionization from HOMO with p character related to the p electrons of the C20@C25 of ring A (Table S6). Because of this similarity, it is reasonable to shift the calculated spectrum of dexamethasone to higher binding energy by +0.465 eV. Based on this assignment, the C@C bond of ring A is the most probable reactive region of this steroid. The second ionization band is mainly related to the ionization from HOMO-2 with the nonbonding character. As seen in Table S6, the energy order of HOMO-1 and HOMO-2 has been reversed in dexamethasone because of electronic correlations. HOMO-2 is related to the lone electron pairs of oxygen atom of ring A. The third ionization band is related to HOMO-1 which is related to the p electrons of the other C@C bond of ring A (C24@C27) (see Table S6). It is interesting to notice that the ionization energy of two C@C bonds of dexamethasone are different from each other. The fourth ionization band is due to the ionization from HOMO-3. HOMO-3 is a nonbonding orbital related to the lone electron pairs of oxygen atoms of OH group connected to ring D, carbonyl bond of a-hydroxy carbonyl group, r electrons of CAC bonds of ring D and a-hydroxy carbonyl group. Based on the assignment of the calculated photoelectron spectrum, ring A of steroid (especially the C@C bond) is the most probable reactive region of dexamethasone. For more confirmation, the shapes of the canonical molecular orbitals of dexamethasone have been demonstrated in Fig. 10a. It is seen that HOMO, HOMO-1 and HOMO-2 are mostly localized on the ring A of steroid while, HOMO-3 and HOMO-4 are mainly concentrated on rings C and D. Estradiol It is an estrogenic steroid which is primary female sex hormones. Estrogens are used as part of some oral contraceptives, in estrogen replacement therapy for postmenopausal women, and in hormone replacement therapy for trans women. It is the predominant estrogen during reproductive years both in terms of
77
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Fig. 8. The canonical molecular structures of (a) dexamethasone, (b) estradiol and (c) cholesterol.
(nO(O-H); ring A)
π
π π
π
c
Intensity (arb.uni)
absolute serum levels as well as in terms of estrogenic activity. During menopause, estrone is the predominant circulating estrogen and during pregnancy estriol is the predominant circulating estrogen in terms of serum levels. Estradiol has only one conformer (Fig. 8b). The ring A of this steroid is a phenyl ring unlike the previous steroids and there are two OH group connected to rings A and C. There is no theoretical and experimental report on the gas phase photoelectron spectrum of estradiol in the literature. Therefore, it is worthwhile to have information about the electronic structure of this steroid in the gas phase. Fig. 9 (spectrum c) shows the calculated photoelectron spectrum of estradiol. The first and second ionization bands of estradiol are related to the ionization from HOMO and HOMO-1, respectively (Table S7). HOMO and HOMO-1 originate from the electrons present in p and p* bonding orbitals of phenyl ring (pc = c and p*c = c). Therefore, the phenyl ring is the most reactive region of this steroid. As shown in Fig. 10b, HOMO and HOMO-1 have been localized on the phenyl ring. The third ionization band is due to HOMO-3 with r character due to the rCAC and rCAH. It is interesting to notice that the first and second ionization of this steroid is not related to the lone electron pairs of oxygen atoms. One important point in the photoelectron spectrum of estradiol is that the energy gap between the second and third ionization band is considerable which is related to the nature of the orbitals involved in the ionization. The forth ionization band of this steroid is related to the ionization of the lone electron pairs of oxygen atom of OH group connected to the phenyl ring. It is important to notice that the ionization of this steroid from the lone electron pairs of oxygen atom of ring D does not take place below 11 eV. To have estimation about the energy shift of the calculated photoelectron spectrum of estradiol, the energy of the first ionization band of phenol (8.35 eV), with the assignment similar to the first ionization band
b
(nO(C=O) ; ring A)
π π
a
13
12
11
10
9
8
7
6
Binding energy (eV) Fig. 9. The calculated photoelectron spectra of (a) dexamethasone, (b) cholesterol and (c) estradiol obtained at the SAC–CI SD-R theory. The spectrum of dexamethasone has been shifted as +0.465 eV.
78
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Fig. 10. The canonical molecular orbitals of (a) dexamethasone, (b) estradiol and (c) cholesterol.
of estradiol, can be considered for this purpose. The first ionization energy of estradiol is 7.734 eV and the calculated spectrum of estradiol can be shifted by 0.575 eV to the higher binding energy. Cholesterol In humans, all steroid hormones are derived from cholesterol. The production of the hormones involves a number of precise modifications to the cholesterol structure, with different series of modifications occurring in different pathways. Cholesterol is in turn synthesized de novo from acetate (90%) or obtained from the diet (10%). Cholesterol is mainly produced and stored in the liver, and is transported to the cells in the form of high density lipoprotein (HDL) and low density lipoprotein (LDL). In normal individuals, both the synthesis of cholesterol and its uptake into the target cells are tightly regulated. Therefore knowing its electronic structures by calculating its photoelectron spectrum is important. The only photoelectron spectrum of cholesterol, reported in the literature,
is related to Ballard et al. work which measured the spectrum of film of cholesterol on hydroxypropionitrile solution running down a tungsten rod [8]. Cholesterol has eight conformers (see Fig. S5) and only one of them is populated in the gas phase based on the calculations in this work. Fig. 9b shows the calculated photoelectron spectrum of this steroid and Table S8 reports the main configuration of the ionic states and related NBO results of cholesterol. It is seen that the Koopmans’ theorem is valid for cholesterol. At the first glance, there are two sites for ionization of this molecule (pc = c and lone electron pairs of OH group). Theoretical calculations show that the first ionization band of this steroid is related to pc = c and the ionization of the lone electron pairs of oxygen does not take place below 10.00 eV. The second, third, fourth and fifth ionization bands of cholesterol are related to HOMO-1, HOMO-2, HOMO-3 and HOMO-4, respectively. These molecular orbitals have r character due to the rCAC and rCAH which are related to rings B, C and D of molecule. The most probable reactive region of this steroid is
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
ring B based on the assignment of the first ionization band (Table S8). This means that this ring is under attack when cholesterol is converted to the other hormones in the body. This conclusion is in agreement with the different modifications of cholesterol based on the different attack sites reported in the literature [37]. The canonical molecular orbitals of cholesterol have been shown in Fig. 10c. Conclusion In this work, the photoelectron spectra of some famous steroids were calculated by considering the electron correlations. The SAC– CI-SD-R method was used for calculating the ionization energies and photoelectron spectra. Using a basis set larger than 6311++G(2df,pd), along with the SAC–CI method was not possible in our work because of the big size of steroids and high cost calculations at the SAC–CI level of theory. The calculated photoelectron spectra of steroids were assigned and active regions of the selected steroids were determined. It was observed that the assignment of the ionization bands of steroids is very sensitive to molecular structure so that a negligible change of composition and/or conformation, yields changes in the assignments of ionization bands and creates dramatic changes of modes of action of steroid. In addition, the number and kind of conformers of the selected steroids which have contribution in their photoelectron spectra were specified. Acknowledgment The authors thank form Isfahan University of Technology (IUT) for financial support and national high performance computing center of IUT. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.molstruc.2014. 07.040. References [1] F. Stanczyk, Glob.libr.women’smed., (ISSN: 1756-2228), 2009, doi:http:// dx.doi.org/10.3843/GLOWM.10278. [2] C. Kubli-Garfias, J. Mendieta, R. Vazquez, J. Mol. Struct. (Theochem) 388 (1996) 35–41.
79
[3] G. Goodman, The Pharmacological Basis of Therapeutics, Pergamon Press, New York, 1990, p. 1157. [4] E. Heftman, Steroid Biochemistry, vol. 15, Academic Press, New York, 1970. p. 200. [5] J.E. Dumont, Action of Ho Press Oxford, 1971, pp. 519–534. [6] Y. Takahata, R. Vendrame, J. Mol. Struct. (Theochem) 391 (1997) 169–178. [7] T. Cvitas, B. Kovac, Lj. Pasa-Tolic, B. Ruscic, L. Klasinc, J.V. Knop, N.S. Bhacca, S.P. McGlynn, Pure Appl. Chem. 61 (1989) 2139–2150. [8] R.E. Ballard, J. Jones, D. Read, A. Inchley, Chem. Phys. Lett. 135 (1987) 119–122. [9] L.J. Pasa-Tolic, B. Kovac, L. Klasinc, J.V. Knop, C. Kubli-Garfias, S.P. McGlynn, L.J. Pasa-Tolic, Croat. Chem. Acta 62 (1991) 813–823. [10] N.S. Bhacca, L. Klasinc, B. Kovac, K. Mihanic, Steroids 61 (1996). [11] Y. Takahata, R. Vendrame, J. Braz. Chem. Soc 12 (2001). ˇ iC´, N.S. Bhacca, S.P. McGlynn, Int. J. Quantum Chem. 28 [12] L. Klasinc, B. RuŠC (1985) 161–167. [13] I. Novak, B. Kovacˇ, Biophys. Chem. 78 (1999) 233–240. [14] L. Klasinc, H. Spiegl, J.V. Knop, S.P. McGlynn, Int. J. Quantum Chem. 48 (1993) 191–198. [15] L. Klasinc, L. Paša-Tolic´, J.V. Knop, C. Kubli-Garfias, S.P. McGlynn, Croat. Chem. Acta 62 (1989) 813–823. [16] http://www.webbook.nist.gov/chemistry [17] H. Nakatsuji, O. Kitao, T. Yonezawa, J. Chem. Phys. 83 (1985) 723–734. [18] H. Nakatsuji, S. Saito, J. Chem. Phys. 91 (1989) 6205–6214. [19] H. Nakatsuji, M. Ehara, M.H. Palmer, M.F. Guest, J. Chem. Phys. 97 (1992) 2561–2570. [20] H. Nakatsuji, M. Ehara, J. Chem. Phys. 101 (1994) 7658–7671. [21] H. Nakatsuji, J. Hasegawa, M. Hada, J. Chem. Phys. 104 (1996) 2321–2330. [22] M. Ehara, Y. Ohtsuka, H. Nakatsuji, J. Chem. Phys. 226 (1998) 113–123. [23] M. Ehara, H. Nakatsuji, Chem. Phys. Lett. 282 (1998) 347–354. [24] H. Farrokhpour, F. Fathi, Comput. Chem. 32 (2011) 2479–2491. [25] H. Farrokhpour, F. Fathi, N.D. Brito, J. Phys. Chem. A 116 (2012) 7004–7015. [26] F. Fathi, H. Farrokhpour, Chem. Phys. Lett. 565 (2013) 102–107. [27] H. Nakatsuji, Chem. Phys. Lett. 177 (1991) 331–337. [28] H. Nakatsuji, J. Chem. Phys. 83 (1985) 713–722. [29] H. Nakatsuji, J. Chem. Phys. 83 (1985) 5743–5748. [30] R.L. Martin, D.A. Shirley, J. Chem. Phys. 64 (1976) 3685–3689. [31] E.D. Glendening, J.K. Badenhoop, A.E. Reed, J.E. Carpenter, J.A. Bohmann, C.M. Morales, F. Weinhold, NBO Version 5.0, Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2001. [32] M.J. Frisch, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford CT, 2009. [33] http://pubchem.ncbi.nlm.nih.gov/. [34] T. Koopmans, Physica 1 (1934) 104–113. [35] www.evolutionary.org. [36] A. Albrecht et al., Neuropsychopharmacology 38 (2013) 286–394. [37] R.M. Evans, Science 240 (1988) 889–894.
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Symmetry adapted cluster–configuration interaction calculation of the photoelectron spectra of famous biological active steroids Fatemeh Abyar, Hossein Farrokhpour ⇑ Chemistry Department, Isfahan University of Technology, Isfahan 84156-83111, Iran
g r a p h i c a l a b s t r a c t
h i g h l i g h t s Gas phase ionization energies of
important steroids were calculated. Population ratios of conformers of BWP
Intensity (arb.uni)
each steroid were calculated in the gas phase. Ten ionization energies were calculated for each steroid. The spectral bands of each steroid were assigned by NBO calculations. The calculated photoelectron spectra were in good agreement with the experiment.
14
13
12
11
10
9
8
Binding Energy (eV)
a r t i c l e
i n f o
Article history: Received 29 June 2014 Received in revised form 15 July 2014 Accepted 15 July 2014 Available online 22 July 2014 Keywords: Ionization energy Steroids Photoelectron spectroscopy SAC–CI NBO Cholesterol
a b s t r a c t The photoelectron spectra of some famous steroids, important in biology, were calculated in the gas phase. The selected steroids were 5a-androstane-3,11,17-trione, 4-androstane-3,11,17-trione, cortisol, cortisone, corticosterone, dexamethasone, estradiol and cholesterol. The calculations were performed employing symmetry-adapted cluster/configuration interaction (SAC–CI) method using the 6311++G(2df,pd) basis set. The population ratios of conformers of each steroid were calculated and used for simulating the photoelectron spectrum of steroid. It was found that more than one conformer contribute to the photoelectron spectra of some steroids. To confirm the calculated photoelectron spectra, they compared with their corresponding experimental spectra. There were no experimental gas phase HeAI photoelectron spectra for some of the steroids of this work in the literature and their calculated spectra can show a part of intrinsic characteristics of this molecules in the gas phase. The canonical molecular orbitals involved in the ionization of each steroid were calculated at the HF/6-311++g(d,p) level of theory. The spectral bands of each steroid were assigned by natural bonding orbital (NBO) calculations. Knowing the electronic structures of steroids helps us to understand their biological activities and find which sites of steroid become active when a modification is performing under a biological pathway. Ó 2014 Elsevier B.V. All rights reserved.
Introduction Generally, steroids are known as hormones in biology. Hormones are materials which are produced at one site in the body ⇑ Corresponding author. Tel.: +98 311 3913243; fax: +98 311 3912350. E-mail addresses: (H. Farrokhpour).
[email protected],
http://dx.doi.org/10.1016/j.molstruc.2014.07.040 0022-2860/Ó 2014 Elsevier B.V. All rights reserved.
[email protected]
of organism and acts at the other site. All steroid hormones are derived from cholesterol by a number of precise modifications to the cholesterol structure, with different series of modifications occurring in different pathways [1]. The main skeleton of molecular structure of steroid is composed of the ring system of three cyclohexanes and one cyclopentane in a fused ring system and different functional groups can be attached to this fused ring system [2] (see Scheme 1). The biological activities of steroids depend on
70
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
F
Scheme 1. Simple basic molecular structure of steroids considered in this work.
their structures [3–5] so that a little change in their molecular structures vary the number of populated conformers of steroid in the gas phase and yields dramatic changes of intensity and modes of action [6]. Change in the action of steroid has direct correlation with its electronic structure. Another important aspect of steroids which has direct correlation with their electronic structure is finding the region of steroid which can be attacked in biological pathways. One of the best methods to obtain information about the electronic structures of molecules is photoelectron spectroscopy. Among the considered steroids in this work, there are only the experimental gas phase HeAI photoelectron spectra for 5a-androstane-3,11,17-trione [7], corticosterone [8] and a thin film of cholesterol on hydroxypropionitrile solution running down a tungsten rod [9] in the literature. There are a limited number of theoretical works on the electronic structure of steroids in the literature which they use semi-empirical methods for calculating the ionization and molecular orbital energies of different series of steroids [7–15]. The semi-empirical methods used in this context are AM1, MNDO and HAM/3. The only ab initio calculation on the electronic structure of steroids is related to the work of Pasa-Tolic et al. [9]. which performed simple ab initio calculations on 5a-androstane steroid by self-consistent field (SCF) method using a very small basis set (STO-3G). It should be mentioned that the electronic correlations which are important in the energy order of molecular orbitals of each compound are absent in the computational methods used for the steroids in the literature. The selected steroids in this work are 5a-androstane-3,11,17-trione, 4-androstane-3,11,17-trione, cortisol, cortisone, corticosterone, dexamethasone, estradiol and cholesterol. One of the motivations for calculating the ionization energies of the steroids in this work is that the electronic structure of steroid is an important factor in determining its biological activities. Therefore, calculating the ionization energies of steroids and assigning their photoelectron spectra helps us to understand their electronic structures and find the most probable ionization sites in them relevant to their biological activities. The other motivation is that there is no report, experimentally and theoretically, on the gas phase ionization energies of some considered steroids in this work
Intensity (arb.uni)
E
D
C
B A
(nO(C=O); ring A)
(nO(C=O); ring C and D)
a nO(C=O); ring C and D (nO (C=O) ; ring D, C;πC=C) (nO (C=O) ; ring A; πC=C) πC=C
b 14
13
12
11
10
9
8
7
Binding Energy (eV) Fig. 2. (a) The experimental HeAI photoelectron spectrum of 5a-androstane3,11,17-trione [6] (black solid line) compared with its calculated photoelectron spectrum obtained using SAC–CI SD-R/6-311++G(2df,pd) level of theory (blue solid line). The calculated spectrum has been shifted as +0.8 eV (see ‘5a-Androstane3,11,17-trione’). (b) Red trace shows the simulated photoelectron spectrum of 4androstene-3,11,17-trione obtained at the same level of theory. Vertical lines show the energy position and intensity of the calculated ionization bands. The arrows in the figure show the assignment of the selected ionization bands. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
except for 5a-androstane-3,11,17-trione and corticosterone. Some of the steroids have a lot of conformers in the gas phase and using the theoretical calculations with the aid of the experimental photoelectron spectrum, it is possible to understand which conformers have dominant contributions in the spectrum of steroid and are responsible for the biological activity of steroid. The gas phase experimental and theoretical information on the fundamental properties of biological molecules are very important in understanding many biological phenomena and providing insight into the physicochemical origin of the properties of biological molecules. One of the most important physicochemical properties of biomolecules is their ionization potentials which are useful quantum mechanical diagnostics for oxidative potentials of these
Fig. 1. The molecular structures of (a) 5a-androstane-3,11,17-trione and (b) 4-androstene-3,11,17-trione.
71
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Table 1 The ionization energies of steroids, calculated at the SAC–CI-SD-R level of theory using 6-311++G(2df,pd) basis set. The superscript roman letters show the conformer number. Compound 4-Androstene-3,11,17-trione 5a-Andestron-3.11.17-trion Cortisol Cortisone
Corticosterone
Dexamethasone Estradiol Cholesterol a b
I1 (eV) b
7.987(0.906) 8.787a 7.930(0.912) 8.73a 8.516(0.930) 8.981a 8.543(0.910)I 9.008a,I 8.553(0.913)II 9.018a,II 8.525(0.929)I 8.990a,I 8.562(0.928)II 9.027a,II 8.806(0.931) 9.271a 6.622(0.927) 7.197a 7.936(0.94)
I2
I3
I4
I5
8.171(0.895) 8.971 8.301(0.911) 9.101 8.64(0.890) 9.105 8.638(0.915) 9.103 8.654(0.913) 9.119 8.619(0.891) 9.084 8.645(0.891) 9.11 8.937(0.877) 9.402 7.462(0.924) 8.037 8.804(0.93)
8.383(0.920) 9.183 8.713(0.904) 9.513 9.221(0.927) 9.686 8.923(0.911) 9.388 8.912(0.912) 9.377 9.192(0.926) 9.657 9.256(0.926) 9.721 9.260(0.933) 9.725 8.316(0.923) 8.891 9.228(0.93)
8.824(0.903) 9.624 9.341(0.919) 10.141 9.632(0.930) 10.097 9.591(0.922) 10.056 9.784(0.920) 10.249 9.679(0.923) 10.144 9.651(0.920) 10.116 9.479(0.930) 9.944 8.611(0.920) 9.186 9.731(0.937)
9.533(0.917) 10.333 9.798(0.915) 10.598 9.816(0.926) 10.281 10.074(0.927) 10.539 10.080(0.928) 10.545 9.827(0.923) 10.292 9.823(0.926) 10.288 10.235(0.933) 10.7 8.932(0.921) 9.507 9.999(0.938)
Shifted calculated ionization energies. The numbers in parenthesis are the intensity of ionization bands.
molecules. For example, when a photoionization or photoabsorption process occurs in a biological system such as living cells, it may cause certain photobiological effects on the system such as damage, cell death, or mutation. Therefore, knowing the values of ionization energies of biomolecules is important for unraveling the mechanism of protein, DNA, and cell damage due to photoionization. To the best of author knowledge, there is no high level ab initio quantum chemical calculations on the electronic structure for molecules as large as the steroids (fascinating compounds) in the literature. In addition, there is no information about the ionization energies of steroids in the NIST Chemistry Webbook [16]. It was found that a high level ab initio method such as SAC–CI is a proper method for calculating the valence and core ionization of molecules [17–26]. In this work, the ionization energies of the considered steroids are calculated employing SAC–CI method and their calculated photoelectron spectra assigned.
Methodology The SAC–CI-SD-R method which uses the single and double excitation operators along with the 6-311++G(2df,pd) basis set was employed for calculating the ionization energies. This method uses all single excitation operators and the double excitation operators are included when their second-order contribution in energy are larger than a given threshold (k = 10 6; level three) in the SAC calculations to obtain the energy and wave function of the ground state of neutral molecule [27–29]. For unlinked operators, the products of linked operators whose SDCI coefficients of higher than 5 10 3 were also used in the SAC calculations. Optimized geometries and Boltzmann population ratios (BPR) of conformers of each molecule were calculated at the B3LYP/6-31+G(d) level of theory. The calculated BPR of the conformers of each steroid, the calculated ionization cross sections and the ionization energies of each conformer were used to simulate the photoelectron spectrum of each steroid. The ionization cross sections were calculated using the monopole approximation [30], which allows the correct estimation of the relative intensities of ionization bands. For calculating the monopole intensities, the correlated SAC wave function of the ground electronic state of neutral molecule and SAC–CI SD-R wave functions of the related ionic electronic states were used. Furthermore, NBO calculations using Gaussian NBO (version 5)
[31] were performed at the Hartree–Fock (HF)/6-311++G(d,p) level of theory to calculate the canonical and natural bonding molecular orbitals at the ground electronic state for the spectral band assignment. All of the calculations were performed using the Gaussian Quantum Chemistry Package [32]. Result and discussion As mentioned before, there are different conformers for each steroid which some of them can be populated in the gas phase. The molecular structures of conformers of the steroids in this work have been taken form pubchem website [33]. There is complete information about the different conformers of steroids in this website. Figs. S1–S5 (supplementary material) show the molecular structures of conformers of corticosterone, cortisol, cortisone, dexamethasone, and cholesterol taken from pubchem website, respectively. The molecular structures of conformers of each steroid were optimized at the B3LYP/6-31+G(d) level of theory and then frequency calculation were performed on the optimized structures, at the same level of theory, to obtain the population ratio of conformers in the gas phase in the temperature range of 160 to 180°C used for evaporating of steroids, reported in the literature [9]. The population ratios of conformers of the steroids in this work have also been reported in Figs. S1–S5. As seen in Fig. S5 cholesterol has eight conformers and only one of them is populated in the gas phase. Similarly, corticosterone and cortisone have only two populated conformers in the gas phase (Figs. S1 and S3). Cortisol and dexamethasone have only one populated conformer in the gas phase. Pubchem website proposes only one conformer for 5a-androstane-3,11,17-trione, 4-androstane-3,11,17-trione and estradiol. In the next sections, the photoelectron spectrum of each steroid and its assignment are explained, separately. 5a-Androstane-3,11,17-trione The structure of this steroid has been shown in Fig. 1. There is only one experimental photoelectron spectrum for 5a-androstane-3,11,17-trione in the literature [6]. As seen in Fig. 1, at the first glance, there are three oxygen atoms in this steroid containing lone electron pairs and three pC@O (p electrons of C@O bond) which can be considered as ionization sites in this steroid. It is important to know the ionization energy
72
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Fig. 3. The canonical molecular orbitals of (a) 5a-androstane-3,11,17-trione and (b) 4-androstene-3,11,17-trione.
order of these sites. Fig. 2 compares the calculated photoelectron spectrum of 5a-androstane-3,11,17-trione (blue spectrum in Fig. 2) with its experimental photoelectron spectrum (black spectrum in Fig. 2) [7]. It can be seen that the simulated spectrum of 5a-androstane3,11,17-trione can describe the three feature A, B and C of the experimental spectrum well. Unfortunately, the resolution of the reported experimental spectrum is not enough to see the other calculated features in it. It seems that there is considerable background in the experimental spectrum for the binding energies higher than 10 eV. In this case, theoretical calculations are useful to distinguish the ionization bands in the region of the photoelectron spectrum which is not resolved. The simulated spectrum of this steroid has been shifted by +0.8 to higher binding energy for matching with the experimental spectrum. It should be mentioned that although, the value of energy shift is relatively large because of the size of molecule but, comparison of the shifted spectrum
with the experimental spectrum confirms that the SAC–CI method can relatively well predict the relative energy positions of the ionization bands. Table 1 reports the calculated ionization energies of 5a-androstane-3,11,17-trione and the corresponding ionization energies considering +0.8 eV energy shift. Comparison of the experimental spectrum with the theoretical spectrum shows that features A, B and C of the experimental spectrum are composed of one ionization band, separately. Table S1 tabulated the main configuration of the ionic states and the dominant natural bonding orbital contributions in the canonical orbitals involved in the ionization for 5a-androstane3,11,17-trione. The first ionization band of 5a-androstane3,11,17-trione (feature A) is related to the ionization from HOMO with nonbonding character due to the lone electron pairs of oxygen of carbonyl bonds of rings C and D (Table S1; Fig. 2). The second ionization originates from HOMO-1 with nonbonding character but, because of the lone electron pairs of oxygen atom of carbonyl
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
conformer I (%25.3)
73
conformer I (%59)
conformer II (%74)
conformer II (%41)
(b)
(a)
(c) Fig. 4. The molecular structures of (a) the conformers of corticosterone, (b) the conformers of cortisone and (c) cortisol.
group of ring A. It is seen that the ionization energy of the lone electron pairs of oxygen atom of ring A is higher than that of the oxygen atoms of rings C and D. The assignment of the third ionization band, due to the ionization from HOMO-2, is mainly related to the nonbonding electrons of oxygen atom of ring D. The forth and fifth ionization bands are related to the ionization from HOMO-3 and; HOMO-4 and HOMO-5 orbitals, respectively. These molecular orbital have mainly r character due to CAC and CAH bonds (see Table S1). It is evident from Table S1 that the Koopmans’ theorem [34] is nearly valid for the considered assigned ionization bands of this steroid because the energy order of molecular orbitals of this steroid for ionization is HOMO > HOMO-1 > HOMO-2 > HOMO3 > HOMO-4. The main configuration of the wave functions of the first, second, third and fourth ionization bands of 5a-androstane3,11,17-trione are single HF ionized determinants (Table S1) which
shows that the electron correlations in these ionic states are not intense. The shape of the canonical molecular orbitals of 5a-androstane-3,11,17-trione have been shown in Fig. 3. The assignment of the photoelectron spectrum of this steroid and the shape of the HOMO of this steroid (Fig. 3) shows that the most probable reactive regions of this steroid are rings C and D (especially oxygen atoms) which are important in the biological activity of this steroid. 4-Androstane-3,11,17-trione (adrenosterone) Adrenosterone is a prohormone and its conversion hormone is known as 11-ketotestosterone, which is quite an interesting hormone, being a mild androgen in humans and a sex steroid in fish. 11-oxo is a non-aromatizing analog of testosterone, which causes dry lean gains and fat loss, along with an increased sexual desire
74
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
5a-androstane-3,11,17-trione have been shown in Fig. 3. Therefore, the most probable reactive region of this steroid is rings C and D (oxygen atoms) but, there is also some reactivity in ring A due to C@C bond. The wave function of the second ionic state is a linear combination of HOMO and HOMO-2 (major contribution). HOMO-2 is mostly related to the lone electron pairs of oxygen atom connected to ring A. Similar to the first ionization band, the ionization of the steroid from the p electrons of C@C bond can also take place in the second ionization band. It should be mentioned that the ionization probability of this steroid from the lone electron pairs of oxygen atom in the first and second ionization bands is about six times higher than the ionization from C@C bond. The wavefunction of the third ionic state is a linear combination of three HF ionized determinant related to HOMO (major contribution), HOMO-1 and HOMO-2. Table S2 shows that the ionization of steroid from the p electrons of C@C bond mainly occurs in the third ionization band. The ionization probability from HOMO is about five times higher than that of HOMO-1 and HOMO-2 in the third ionization band. Finally, it should be mentioned that the ionization of the p electrons of C@O bonds of 4-androstane-3,11,17trione and 5a- androstane-3,11,17-trione does not take place below 11 eV.
F E D C
Intensity (arb.uni)
B
A
BWP total
(nO(O-H) ; ring D) (nO(C=O) ; ring A)
π conformer 2
conformer 1
Corticosterone 14
13
12
11
10
9
8
Binding Energy (eV) Fig. 5. The experimental HeAI photoelectron spectrum of corticosterone [9] (black solid line) compared with its Boltzmann weighted photoelectron (BWP) spectrum (green trace) calculated at the SAC–CI SD-R level of theory. Vertical lines show the energy positions of the calculated ionization bands. Traces red and blue show the calculated photoelectron spectra of conformers 1 and 2 of corticosterone, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
[35]. The difference between 4-androstane-3,11,17-trione and 5aandrostane-3,11,17-trione is related to the presence of the unsaturated C@C bond in the 4-androstane-3,11,17-trione. As shown in Fig. 2, The shape of the calculated photoelectron spectrum of 4-androstane-3,11,17-trione (red spectrum) is different from 5a-androstane-3,11,17-trione although, there are similarity between their molecular structures. It is seen that the first, second and third ionization bands of this steroid form one feature in the calculated spectrum. There is no experimental photoelectron spectrum for this steroid in the literature for comparing with the theoretical spectrum. Table S2 tabulated the main configurations of the ionic wave functions (obtained from SAC–CI calculations) and the dominant natural bonding orbital contributions in the canonical orbitals involved in the ionization for 4-androstane3,11,17-trione. Comparison of Table S2 with S1 shows that the amount of the electronic correlations in 4-androstane-3,11,17-trione is higher than that in 5a-androstane-3,11,17-trione because the wave function of the first, second and third ionic states are linear combination of two or three HF single ionized determinants. Therefore, the Koopmans’ theorem is not valid for 4-androstane3,11,17-trione. The first ionization band of 4-androstane-3,11,17-trione is related to the ionization from HOMO and HOMO-1 (major contribution) with different contributions (Table S2). Therefore, the first ionization of this steroid takes place from HOMO-1 unlike to what was seen for 5a-androstane-3,11,17-trione. HOMO has p character due to the p electrons of C@C bond of ring A and HOMO-1 is mostly related to the lone electron pairs of oxygen atoms of rings A, D and C (especially rings C and D). Therefore, there is probability of the ionization of this steroid from the C@C bond of ring A in the first ionization band. The shape of the canonical molecular orbitals of
Corticosterone is an adrenocortical steroid that has modest but significant activities as a mineralocorticoid and a glucocorticoid. It has multiple effects on memory. The main effects are seen through the impact of stress on emotional memories as well as long term memory (LTM) [36]. There are three conformers for this steroid (see Fig. S1) which two of them are populated in the gas phase based on the thermochemistry calculations (Fig. 4). The difference between two populated conformers in gas phase is related to the rotation of a-hydroxy carbonyl group connected to ring D. The population ratio of conformer II is higher than that of conformer I (Fig. 4). Fig. 5 shows the calculated spectra of the conformers of corticosterone along with its BWP spectrum. The BWP spectrum has been shifted as +0.465 eV for matching its first feature with the first peak of the experimental spectrum (feature A). The agreement between the BWP spectrum and the experimental spectrum [9] is well. The relative energy positions of the calculated ionization bands of conformer I are nearly similar to that of conformer II for the binding energies below 11 eV. The assignment of the experimental photoelectron spectrum of corticosterone is performed based on the SAC–CI and NBO results of conformer II (Table S3) because of its higher population. Feature A of the experimental spectrum composed from the first ionization bands of conformers I and II. The first ionization band of conformer II originate from HOMO with p character due to the C@C bond of ring A. It is seen that the assignment of the first ionization band of this steroid is different to what was seen for 4-androstane3,11,17-trione (ionization of lone electron pairs of oxygen atom of rings D and C). The second ionization band is related to the nonbonding electrons of oxygen atom of ring A (HOMO-1). Therefore, the most probable reactive region of this steroid is the C@C bond of ring A. The third ionization band is related to HOMO-2 which has mainly r character although, there are some contributions from the lone electron pairs of the oxygen atoms of ring C and ahydroxy carbonyl group of ring D (Table S3). Similar assignment is valid for the fourth ionization band (ionization from HOMO-3). It is interesting to notice that the ionization of this steroid from the oxygen sites does not take place in the third and fourth ionization bands of this steroid unlike to what was seen for the previous steroids. The sixth ionization band is related to the ionization of the lone electron pairs of OH group of a-hydroxy carbonyl group of ring D and corresponds to feature D in the experimental spec-
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
75
Fig. 6. The canonical molecular orbitals of (a) corticosterone, (b) cortisone and (c) cortisol.
trum. It is evident from Table S3 that the Koopmans’ theorem is nearly valid for the first, second and third ionization bands of this steroid. The wave function of the fourth and fifth ionization bands are a linear combination of HOMO-3 and HOMO-4 with different contributions which shows that the electronic correlations have been increased in these ionic states. The assignment of the ionization bands of conformer I of corticosterone and the shape of its canonical molecular orbitals is similar to conformer II. Fig. 6a shows the canonical molecular orbitals of conformer II of corticosterone. Cortisone Cortisone is one of the main hormones released by the adrenal gland in response to stress. In addition, it is used to treat a variety of aliments and can be administered intravenously, orally, intraarticularly or transcutaneously. Similar to corticosterone, cortisone has three conformers (see Fig. S2) and only two of them are populated in the gas phase (Fig. 4b). The difference between cortisone and cortisol is related to the conversion of C@O bond to CAOH
bond in ring C. Fig. 7 shows the calculated photoelectron spectra of two conformers of cortisone. Comparison of Table S4 with S3 shows that the amount of electron correlation in the first, second and third ionic states of cortisone are higher than that for cortisol because the wave functions of these ionic states are a linear combination of single ionized HF determinants. The wave function of the first ionic state of cortisone is a linear combination of two single ionized determinants related to HOMO and HOMO-1 with the contributions comparable with each other (see Table S4). This means that the ionization from HOMO and HOMO-1 takes place in the first ionization bands with the nearly same probability. HOMO is mostly localized on the C@C bond of ring A and HOMO-1 is mostly due to the lone electron pairs of oxygen atom of ring A. Therefore, the most probable region for the biological activity of this steroid is ring A (oxygen atom and C@C bond) while, the first ionization band of corticosterone is only related to the C@C bond of ring A. The second ionization band is a linear combination of three ionized HF determinants related to HOMO, HOMO-1 and HOMO-2. Similar to HOMO-1, HOMO-2 has been localized more on the oxygen atoms of rings A and C com-
76
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
(nO(C=O) ; ring A)
of ring A. Therefore, it is reasonable to shift the calculated spectrum of cortisol by +0.465 eV to the higher binding energy although there is no experimental spectrum for this steroid in the literature. The first feature in the calculated spectrum contains of two ionization bands. The assignment of the second ionization bands of cortisol is same as that of corticosterone (Table S5). Therefore, the first and second ionization takes place in the ring A of steroid and the most probable reactive region of this steroid is ring A (especially C@C bond). Fig. 6c shows that there is similarity between the canonical molecular orbitals of cortisol and corticosterone. It is evident from Table S5 that the amount of the electronic correlation in cortisol is small compared to corticosterone and cortisone and the Koopmans’ theorem is completely valid for it. Fig. 6c shows that HOMO-2, HOMO-3 and HOMO-4 are completely distributed on the molecule and they are not localized on the special region of molecule. HOMO-3 is slightly localized on the a-hydroxy carbonyl group.
πC=C
Intensity (arb.uni)
d
BWP spectrum
c
b
Dexamethasone
conformer 2
(nO(C=O) ; ring D)
(nO(C=O) ; ring A ,C; π
a conformer 1 14
13
12
11
10
9
8
7
Binding Energy (eV) Fig. 7. The calculated photoelectron spectra of conformers of cortisone (spectrum a and b) along with their Boltzmann-weighted photoelectron spectrum (labeled with ‘‘BWP’’ in the figure) obtained at the SAC–CI SD-R level of theory. Trace d shows the calculated photoelectron spectrum of cortisol. The arrows in the figure show the assignment of the selected ionization bands.
pared to other regions of molecule. Fig. 6b shows that the localization of the HOMO-2 on the oxygen atom of ring A in cortisone is higher than corticosterone. Table S4 shows that the ionization probability of steroid from C@C bond in the second ionization band is more than the first one because the contribution of the single ionized HF determinant relevant to HOMO is higher than the other determinants in the wave function of the second ionic state. The wavefunction of the third ionization band is mostly related to HOMO-2 but there is some contribution from HOMO. Therefore, there is also probability of ionization of p electrons of C@C bond in this ionization band. It is seen that the first, second and third ionization bands have similar assignment. The wave function of the fourth ionization band is composed of only one single ionized HF determinant related to the ionization from HOMO-3. HOMO-3 is mostly related to the oxygen of carbonyl of a-hydroxy carbonyl group connected to ring D. The difference between the HOMO-3 of cortisone and corticosterone is related to the localization of orbital on ring A and B (see Fig. 6). Cortisol Cortisol is a hormone which is released in response to stress and a low level of blood glucocorticoid. It has three conformers (see Fig. S3) which only one of them is the most stable conformer in the gas phase (Fig. 4c). Fig. 7 shows the calculated photoelectron spectrum of cortisol and its ionization energies have been reported in Table 1. There is no experimental photoelectron spectrum for cortisol in the literature for comparing with the theory. Therefore, it is worthwhile to have information about its photoelectron spectrum from the theoretical calculations. As shown in Table S5, similar to corticosterone, the first ionization of this steroid is due to the ionization of HOMO related to the p electrons of C@C bond
Dexamethasone has anti-inflammatory and immunosuppressant effects and it is on the World Health Organizations (WHO) list of Essential Medicines (Fig. 8). Dexamethasone have two conformers (see Fig. S4) and only one of them is populated in the gas phase (Fig. 8a). There is no theoretical and experimental report on the gas phase photoelectron spectrum of dexamethasone in the literature. The calculated photoelectron spectrum of dexamethasone has been shown in Fig. 9 (spectrum a). As seen in Table S6, the wavefunctions of the ionic states of dexamethasone are composed of single ionized HF determinants. Similar to corticosterone, the first ionization band of dexamethasone is related to the ionization from HOMO with p character related to the p electrons of the C20@C25 of ring A (Table S6). Because of this similarity, it is reasonable to shift the calculated spectrum of dexamethasone to higher binding energy by +0.465 eV. Based on this assignment, the C@C bond of ring A is the most probable reactive region of this steroid. The second ionization band is mainly related to the ionization from HOMO-2 with the nonbonding character. As seen in Table S6, the energy order of HOMO-1 and HOMO-2 has been reversed in dexamethasone because of electronic correlations. HOMO-2 is related to the lone electron pairs of oxygen atom of ring A. The third ionization band is related to HOMO-1 which is related to the p electrons of the other C@C bond of ring A (C24@C27) (see Table S6). It is interesting to notice that the ionization energy of two C@C bonds of dexamethasone are different from each other. The fourth ionization band is due to the ionization from HOMO-3. HOMO-3 is a nonbonding orbital related to the lone electron pairs of oxygen atoms of OH group connected to ring D, carbonyl bond of a-hydroxy carbonyl group, r electrons of CAC bonds of ring D and a-hydroxy carbonyl group. Based on the assignment of the calculated photoelectron spectrum, ring A of steroid (especially the C@C bond) is the most probable reactive region of dexamethasone. For more confirmation, the shapes of the canonical molecular orbitals of dexamethasone have been demonstrated in Fig. 10a. It is seen that HOMO, HOMO-1 and HOMO-2 are mostly localized on the ring A of steroid while, HOMO-3 and HOMO-4 are mainly concentrated on rings C and D. Estradiol It is an estrogenic steroid which is primary female sex hormones. Estrogens are used as part of some oral contraceptives, in estrogen replacement therapy for postmenopausal women, and in hormone replacement therapy for trans women. It is the predominant estrogen during reproductive years both in terms of
77
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Fig. 8. The canonical molecular structures of (a) dexamethasone, (b) estradiol and (c) cholesterol.
(nO(O-H); ring A)
π
π π
π
c
Intensity (arb.uni)
absolute serum levels as well as in terms of estrogenic activity. During menopause, estrone is the predominant circulating estrogen and during pregnancy estriol is the predominant circulating estrogen in terms of serum levels. Estradiol has only one conformer (Fig. 8b). The ring A of this steroid is a phenyl ring unlike the previous steroids and there are two OH group connected to rings A and C. There is no theoretical and experimental report on the gas phase photoelectron spectrum of estradiol in the literature. Therefore, it is worthwhile to have information about the electronic structure of this steroid in the gas phase. Fig. 9 (spectrum c) shows the calculated photoelectron spectrum of estradiol. The first and second ionization bands of estradiol are related to the ionization from HOMO and HOMO-1, respectively (Table S7). HOMO and HOMO-1 originate from the electrons present in p and p* bonding orbitals of phenyl ring (pc = c and p*c = c). Therefore, the phenyl ring is the most reactive region of this steroid. As shown in Fig. 10b, HOMO and HOMO-1 have been localized on the phenyl ring. The third ionization band is due to HOMO-3 with r character due to the rCAC and rCAH. It is interesting to notice that the first and second ionization of this steroid is not related to the lone electron pairs of oxygen atoms. One important point in the photoelectron spectrum of estradiol is that the energy gap between the second and third ionization band is considerable which is related to the nature of the orbitals involved in the ionization. The forth ionization band of this steroid is related to the ionization of the lone electron pairs of oxygen atom of OH group connected to the phenyl ring. It is important to notice that the ionization of this steroid from the lone electron pairs of oxygen atom of ring D does not take place below 11 eV. To have estimation about the energy shift of the calculated photoelectron spectrum of estradiol, the energy of the first ionization band of phenol (8.35 eV), with the assignment similar to the first ionization band
b
(nO(C=O) ; ring A)
π π
a
13
12
11
10
9
8
7
6
Binding energy (eV) Fig. 9. The calculated photoelectron spectra of (a) dexamethasone, (b) cholesterol and (c) estradiol obtained at the SAC–CI SD-R theory. The spectrum of dexamethasone has been shifted as +0.465 eV.
78
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
Fig. 10. The canonical molecular orbitals of (a) dexamethasone, (b) estradiol and (c) cholesterol.
of estradiol, can be considered for this purpose. The first ionization energy of estradiol is 7.734 eV and the calculated spectrum of estradiol can be shifted by 0.575 eV to the higher binding energy. Cholesterol In humans, all steroid hormones are derived from cholesterol. The production of the hormones involves a number of precise modifications to the cholesterol structure, with different series of modifications occurring in different pathways. Cholesterol is in turn synthesized de novo from acetate (90%) or obtained from the diet (10%). Cholesterol is mainly produced and stored in the liver, and is transported to the cells in the form of high density lipoprotein (HDL) and low density lipoprotein (LDL). In normal individuals, both the synthesis of cholesterol and its uptake into the target cells are tightly regulated. Therefore knowing its electronic structures by calculating its photoelectron spectrum is important. The only photoelectron spectrum of cholesterol, reported in the literature,
is related to Ballard et al. work which measured the spectrum of film of cholesterol on hydroxypropionitrile solution running down a tungsten rod [8]. Cholesterol has eight conformers (see Fig. S5) and only one of them is populated in the gas phase based on the calculations in this work. Fig. 9b shows the calculated photoelectron spectrum of this steroid and Table S8 reports the main configuration of the ionic states and related NBO results of cholesterol. It is seen that the Koopmans’ theorem is valid for cholesterol. At the first glance, there are two sites for ionization of this molecule (pc = c and lone electron pairs of OH group). Theoretical calculations show that the first ionization band of this steroid is related to pc = c and the ionization of the lone electron pairs of oxygen does not take place below 10.00 eV. The second, third, fourth and fifth ionization bands of cholesterol are related to HOMO-1, HOMO-2, HOMO-3 and HOMO-4, respectively. These molecular orbitals have r character due to the rCAC and rCAH which are related to rings B, C and D of molecule. The most probable reactive region of this steroid is
F. Abyar, H. Farrokhpour / Journal of Molecular Structure 1076 (2014) 69–79
ring B based on the assignment of the first ionization band (Table S8). This means that this ring is under attack when cholesterol is converted to the other hormones in the body. This conclusion is in agreement with the different modifications of cholesterol based on the different attack sites reported in the literature [37]. The canonical molecular orbitals of cholesterol have been shown in Fig. 10c. Conclusion In this work, the photoelectron spectra of some famous steroids were calculated by considering the electron correlations. The SAC– CI-SD-R method was used for calculating the ionization energies and photoelectron spectra. Using a basis set larger than 6311++G(2df,pd), along with the SAC–CI method was not possible in our work because of the big size of steroids and high cost calculations at the SAC–CI level of theory. The calculated photoelectron spectra of steroids were assigned and active regions of the selected steroids were determined. It was observed that the assignment of the ionization bands of steroids is very sensitive to molecular structure so that a negligible change of composition and/or conformation, yields changes in the assignments of ionization bands and creates dramatic changes of modes of action of steroid. In addition, the number and kind of conformers of the selected steroids which have contribution in their photoelectron spectra were specified. Acknowledgment The authors thank form Isfahan University of Technology (IUT) for financial support and national high performance computing center of IUT. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.molstruc.2014. 07.040. References [1] F. Stanczyk, Glob.libr.women’smed., (ISSN: 1756-2228), 2009, doi:http:// dx.doi.org/10.3843/GLOWM.10278. [2] C. Kubli-Garfias, J. Mendieta, R. Vazquez, J. Mol. Struct. (Theochem) 388 (1996) 35–41.
79
[3] G. Goodman, The Pharmacological Basis of Therapeutics, Pergamon Press, New York, 1990, p. 1157. [4] E. Heftman, Steroid Biochemistry, vol. 15, Academic Press, New York, 1970. p. 200. [5] J.E. Dumont, Action of Ho Press Oxford, 1971, pp. 519–534. [6] Y. Takahata, R. Vendrame, J. Mol. Struct. (Theochem) 391 (1997) 169–178. [7] T. Cvitas, B. Kovac, Lj. Pasa-Tolic, B. Ruscic, L. Klasinc, J.V. Knop, N.S. Bhacca, S.P. McGlynn, Pure Appl. Chem. 61 (1989) 2139–2150. [8] R.E. Ballard, J. Jones, D. Read, A. Inchley, Chem. Phys. Lett. 135 (1987) 119–122. [9] L.J. Pasa-Tolic, B. Kovac, L. Klasinc, J.V. Knop, C. Kubli-Garfias, S.P. McGlynn, L.J. Pasa-Tolic, Croat. Chem. Acta 62 (1991) 813–823. [10] N.S. Bhacca, L. Klasinc, B. Kovac, K. Mihanic, Steroids 61 (1996). [11] Y. Takahata, R. Vendrame, J. Braz. Chem. Soc 12 (2001). ˇ iC´, N.S. Bhacca, S.P. McGlynn, Int. J. Quantum Chem. 28 [12] L. Klasinc, B. RuŠC (1985) 161–167. [13] I. Novak, B. Kovacˇ, Biophys. Chem. 78 (1999) 233–240. [14] L. Klasinc, H. Spiegl, J.V. Knop, S.P. McGlynn, Int. J. Quantum Chem. 48 (1993) 191–198. [15] L. Klasinc, L. Paša-Tolic´, J.V. Knop, C. Kubli-Garfias, S.P. McGlynn, Croat. Chem. Acta 62 (1989) 813–823. [16] http://www.webbook.nist.gov/chemistry [17] H. Nakatsuji, O. Kitao, T. Yonezawa, J. Chem. Phys. 83 (1985) 723–734. [18] H. Nakatsuji, S. Saito, J. Chem. Phys. 91 (1989) 6205–6214. [19] H. Nakatsuji, M. Ehara, M.H. Palmer, M.F. Guest, J. Chem. Phys. 97 (1992) 2561–2570. [20] H. Nakatsuji, M. Ehara, J. Chem. Phys. 101 (1994) 7658–7671. [21] H. Nakatsuji, J. Hasegawa, M. Hada, J. Chem. Phys. 104 (1996) 2321–2330. [22] M. Ehara, Y. Ohtsuka, H. Nakatsuji, J. Chem. Phys. 226 (1998) 113–123. [23] M. Ehara, H. Nakatsuji, Chem. Phys. Lett. 282 (1998) 347–354. [24] H. Farrokhpour, F. Fathi, Comput. Chem. 32 (2011) 2479–2491. [25] H. Farrokhpour, F. Fathi, N.D. Brito, J. Phys. Chem. A 116 (2012) 7004–7015. [26] F. Fathi, H. Farrokhpour, Chem. Phys. Lett. 565 (2013) 102–107. [27] H. Nakatsuji, Chem. Phys. Lett. 177 (1991) 331–337. [28] H. Nakatsuji, J. Chem. Phys. 83 (1985) 713–722. [29] H. Nakatsuji, J. Chem. Phys. 83 (1985) 5743–5748. [30] R.L. Martin, D.A. Shirley, J. Chem. Phys. 64 (1976) 3685–3689. [31] E.D. Glendening, J.K. Badenhoop, A.E. Reed, J.E. Carpenter, J.A. Bohmann, C.M. Morales, F. Weinhold, NBO Version 5.0, Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2001. [32] M.J. Frisch, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford CT, 2009. [33] http://pubchem.ncbi.nlm.nih.gov/. [34] T. Koopmans, Physica 1 (1934) 104–113. [35] www.evolutionary.org. [36] A. Albrecht et al., Neuropsychopharmacology 38 (2013) 286–394. [37] R.M. Evans, Science 240 (1988) 889–894.