A structural study of fentanyl by DFT calculations, NMR and IR spectroscopy

Article abstract of DOI:10.1016/j.molstruc.2016.09.027

N-(1-(2-phenethyl)-4-piperidinyl-N-phenyl-propanamide (fentanyl) is synthesized and characterized by FT-IR, ¹H NMR, ¹³C NMR, mass spectroscopy and elemental analyses. The geometry optimization is performed using the B3LYP and M06 density functionals with 6-311?+?G(d) and 6-311++G(d,p) basis sets. The complete assignments are performed on the basis of the potential energy distribution (PED) of the all vibrational modes. Almost a nice correlation is found between the calculated ¹³C chemical shifts and experimental data. The frontier molecular orbitals and molecular electrostatic potential of fentanyl are also obtained.

Full text of DOI:10.1016/j.molstruc.2016.09.027

Accepted Manuscript
A structural study of fentanyl by DFT calculations, NMR and IR spectroscopy
Zahra Asadi, Mehdi D. Esrafili, Esmail Vessally, Manzarbanou Asnaashariisfahani,
Saeideh Yahyaei, Ali Khani
PII:
S0022-2860(16)30954-1
10.1016/j.molstruc.2016.09.027
MOLSTR 22939
DOI:
Reference:
To appear in: Journal of Molecular Structure
Received Date: 4 May 2016
Revised Date: 9 September 2016
Accepted Date: 9 September 2016
Please cite this article as: Z. Asadi, M.D. Esrafili, E. Vessally, M. Asnaashariisfahani, S. Yahyaei,
A. Khani, A structural study of fentanyl by DFT calculations, NMR and IR spectroscopy, Journal of
Molecular Structure (2016), doi: 10.1016/j.molstruc.2016.09.027.
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ACCEPTED MANUSCRIPT
A structural study of fentanyl by DFT calculations, NMR and IR
spectroscopy
Zahra Asadi*,a, Mehdi D. Esrafili*,b, Esmail Vessally c, Manzarbanou Asnaashariisfahani d, Saeideh Yahyaei e,
Ali Khani e
a Young Researchers and Elite Club, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran
b Laboratory of Theoretical Chemistry, Department of Chemistry, University of Maragheh, Maragheh, Iran
c Department of Chemistry, Payame Noor University, Tehran, Iran
d Department of Chemistry, Islamic Azad University, North Tehran Branch, Tehran, Iran
e Department of Chemistry, Miyaneh branch, Islamic Azad University, Miyaneh, Iran
* Corresponding Author. z.asadi161@gmail.com (Z. Asadi) and esrafili@maragheh.ac.ir (M.D. Esrafili).
Abstract
N-(1-(2-phenethyl)-4-piperidinyl-N-phenyl-propanamide (fentanyl) is synthesized and
characterized by FT-IR, 1H NMR, 13C NMR, mass spectroscopy and elemental analyses. The
geometry optimization is performed using the B3LYP and M06 density functionals with 6-
311+G(d) and 6-311++G(d,p) basis sets. The complete assignments are performed on the
basis of the potential energy distribution (PED) of the all vibrational modes. Almost a nice
13
correlation is found between the calculated C chemical shifts and experimental data. The
frontier molecular orbitals and molecular electrostatic potential of fentanyl are also obtained.
Keywords: opiate agonists; DFT; chemical shifts; M06; B3LYP; MEP.
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1. Introduction
Opiate agonists such as 4-anilidopiperidine derivatives play a significant role in different
alleviation of pain such as post operational, cancer, etc., and are often used in surgical
analgesia and sedation [1,2]. N-(1-(2-phenethyl)-4-piperidinyl-N-phenyl-propanamide
(fentanyl) is an extremely powerful opioid analgesic from this family, which is about 50-100
times more potent than morphine in humans and is described as having a fast onset and a
short duration of action [3].
Due to the importance of fentanyl in the biomedical fields, several synthetic routes have
been suggested for its preparation [4-10]. Most of these methods, however, require multiple
steps and lengthy refluxing reaction conditions. The isolation and purification of the
intermediate compounds are both tedious, and time and energy consuming process. In
addition, it may also reduce overall yield. The aim of this work is to develop an efficient
method for preparation of fentanyl via an one-pot reaction that involves tandem reductive
alkylation and amination reactions in the presence of sodium triacetoxyborohydride (STAB)
followed by N-acylation reaction (Scheme 1). Sodium triacetoxyborohydride is mainly used
as a mild and selective reducing agent. Also this reagent is especially suitable for reductive
amination of aldehydes and ketones [11]. The structural characterization of fentanyl is also
investigated using different experimental and theoretical methods. The theoretical studies are
performed by means of two restricted density functional theory (DFT) methods, i.e. B3LYP
and M06 functionals.
2. Experimental
2.1 General method
The reactions were monitored by TLC and NMR techniques, which indicated that there
were no side products. The TLC plates were prepared from Merck silica gel powder. Melting
points were obtained in open capillary tubes and were measured on an electro-thermal 9200
apparatus. IR spectra were measured on a Perkin-Elmer RXI, FT-IR spectrometer. 1H and 13C
NMR spectra (CDCl3) were recorded on a Bruker 300 DRX Avance instrument at 500.0 and
100.0MHz, respectively. Mass spectra were recorded on a Shimadzu QP 1100 BX mass
spectrometer. The elemental analysis was performed by using a Perkin-Elmer 2400(II)
CHN/O analyzer. The synthetic route is shown in Scheme 1.
< Scheme 1>
2.2. Synthesis
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To a stirred suspension of 4-piperidone monohydrochloride (15.36 g,0.1 mol) in
dichloroethane (450 ml), triethylamine (27.87 ml, 0.2 mol) and phenylacetaldehyde (11.17
ml, 0.1 mol) were added and stirred for half an hour at room temperature under N2.
Thereafter, sodium triacetoxyborohydride (30 g, 0.14 mol) was added to the reaction mixture
with continuous stirring. The reaction mixture was further stirred for 24 h. Aniline (9.12 ml,
0.1 mol), acetic acid (11.53 ml, 0.2 mol) and sodium triacetoxyborohydride (30 g, 0.14 mol)
were then added and again the reaction mixture was stirred for 24 h. Propionyl chloride
(26.16 ml, 0.3 mol) was then added dropwise and the mixture was stirred for 2 h. The
reaction mixture was then diluted with dichloromethane and washed with 4% aqueous
sodium hydroxide solution followed by water. The organic phase was then shaken with 2N
HCl. The organic layer was separated and the aqueous layer was extracted with DCM.
Combined organic phase was dried over sodium sulfate and concentrated to give crude HCl
salt of fentanyl. Crude product was recrystallized with acetone to give white powder of
fentanyl hydrochloride. The salt was treated with 20% NaOH to give fentanyl which was
recrystallized from petroleum ether (bp 60-80 °C). Characterization data are given below.
1
White powder; mp: 69-70°C. Yield: 81%. IR (KBr) (mmax, cm-1): 3057, 1656, 744. H
NMR (500 MHz, CDCl3) δH: 7.42–7.10 (m, 10H, arom); 4.71 (m, 1H); 3.05–3.03 (m, 2H);
2.78–2.75(m, 2H); 2.59–2.56 (m, 2H); 2.23–2.18 (t, 2H, J=11.3Hz); 1.98–1.93 (q, 2H,
J=7.44Hz); 1.85–1.83 (m, 2H); 1.49–1.47 (m, 2H); 1.06–1.03 (t, 3H, J=7.44Hz).13C NMR
(CDCl3) δC: 173.50; 140.24; 138.85; 130.41; 129.24; 128.59; 128.34; 128.21; 125.98; 60.46;
53.08; 52.14; 33.82; 30.56; 28.49; 22.57; 9.58. MS: m/z (%) (EI) 338 (M+, 1), 245 (7.5), 188
(2.5), 189 (5), 146 (12.5), 91(80), 77(42), 57(100). Anal. Calcd for C22H28N2O: C, 78.53; H,
8.39; N, 8.33. Found: C, 78.42; H, 8.05; N, 8.62.
3. Computational details
In the present work, quantum chemical calculations were carried out at different DFT
levels using the Gaussian 03 suites of programs [12]. The structure of fentanyl was optimized
using the M06 and B3LYP density functionals employing 6-311+G(d) and 6-311++G(d,p)
standard basis sets. No symmetry constraints were used during the optimization. Harmonic
frequencies were calculated for this optimization to confirm the existence of a minimum (no
imaginary frequencies) structure. The M06 is a hybrid meta-GGA functional, where the
Hartree–Fock exchange energy is equal to 27% [13]. This density functional has been
parameterized including main group atoms and transition metals, and it implicitly accounts
for “medium-range” electron correlation. The isotopic chemical shielding (σiso) values were
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calculated based on the gauge-independent atomic orbital (GIAO) approach [14]. The 1H and
13C chemical shifts (δ) were then calculated by subtracting the calculated isotopic value of the
shielding tensor σiso,cal from that of TMS: δ= σiso,TMS - σiso,cal. Also, 1H and 13C chemical shifts
of structure were simulated using the GaussView software [15]. The density of states plots
were obtained using the GaussSum program [16]. The molecular electrostatic potential
(MEP) analysis was performed on the 0.001 electrons/Bohr3 contour of the electronic density
using the wave function analysis-surface analysis suite (WFA-SAS) [17].
4. Results and Discussion
4.1. Geometry and atomic charges
The optimized structure of fentanyl is shown in Figure 1. Tables 1-3 list calculated
bond lengths, bond angles and dihedral angles at different levels of theory. The
corresponding experimental data are also given for comparison. In each case, the true
minimum structure is confirmed following an inspection of the frequencies and the IR spectra
obtained after the frequency calculation. The inspection of the data presented in these Tables
1 reveals that the estimated bond lengths at different DFT levels are almost independent of
the method and basis set used. Unless otherwise noted, the following results are referred for
the B3LYP/6-311++G(d,p) and M06/6-311++G(d,p) levels of theory.
< Figure 1>
The experimental carbon-carbon bond lengths of the phenyl group and piperidine ring
of fentanyl are in the range of 1.38–1.40 and 1.52–1.54 Å, respectively [18, 19]. The
B3LYP/6-311++G(d,p) and M06/6-311++G(d,p) methods predict these bond lengths in the
range of 1.39–1.40, 1.53–1.54 Å and 1.38–1.39, 1.52–1.53 Å, respectively. In addition, the
computed bond length of C18−C19 (1.54 Å) at the B3LYP/6-311++G(d,p) level is in good
agreement with the experimental value reported in Table 1. The B3LYP/6-311++G(d,p)
calculations predict the C8−O9 (1.22 Å), C18−N15 (1.45 Å), C12−N7(1.48 Å), C8−N7(1.37
Å), whereas at the M06/6-311++G(d,p) level, these bond lengths are 1.21, 1.44, 1.47, 1.37 Å,
respectively. The correlations between the experimental and calculated bond lengths are
shown in Figure 2. As is evident, almost a good linear correlation is obtained between the
B3LYP/6-311++G(d,p) results and experimental data. This may indicate that the inclusion of
“medium-range” electron correlation in the M06 density functional does not have any
significant influence on the geometry of fentanyl. The estimated bond angles of C20-C19-
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C18, C19-C18-N15, N15-C16-C17, C16-C17-C12 , C17-C12-C13 are 111.9° (110.8°) 113.2°
(113.4°), 110.1° (111.9°), 110.6° (109.7°), 110.3° (110.5°) at the B3LYP (M06) level,
respectively, which are consistent with the experimental data [18, 19]. (Table 2). The
calculated dihedral angles at B3LYP (M06) level for C16-C17-C12-C13, C18-N15-C14-C13
and C12-N7-C1-C2 are -62.1° (-62.8°), 162.0° (163.2°) and -80.7° (-80.6°), respectively,
which are in good agreement with the corresponding experimental values of -54.4°, 167.9°
and -96.3° [19, 20].
<Table 1>
<Table 2>
<Table 3>
<Figure 2>
The calculated Mulliken atomic charges of fentanyl are given in Figure 3 and Table 4.
Except for N7, C13, N15, C20, C2, C6 and C21, all atoms are negatively charged. The largest
value of positive charge is located on the C20 atom, ca. 1.047 e (0.740 e) at the B3LYP
(M06) level. On the other hand, the C12 atom has the most negative charge -0.853 e (-1.570
e) at the B3LYP (M06) level. Besides, the results of Table 4 clearly indicate that the
calculated atomic charges with the M06 level are almost smaller in comparison with those
obtained by the B3LYP, regardless of the basis set used. For a given density functional, the
addition of polarization and diffuse functions to the 6-311+G(d) basis set has a significant
influence on the calculated atomic charges. As also evident from Figure 3, the dipole moment
of fentanyl is oriented perpendicular relative to the piperidine ring. The calculated dipole
moment value (3.2 Debye at both B3LYP and M06 levels) clearly indicate the partial ionic
character of the C=O as well as the C-N bonds and verifies the relatively large charge density
distribution within this molecule.
< Figure 3>
<Table 4>
4.2. Vibrational assignments
The experimental (FT-IR) and simulated vibrational spectra of fentanyl are shown in
Figure 4. According to the theoretical calculations, fentanyl has the C1 point group
symmetry. This compound consists of 53 atoms. The number of vibration normal modes
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of fentanyl is 153 normal vibrational modes, 105 modes of vibrations are in-plane and 47
modes are out-of-plane. The bands that are in the plane of the molecule are represented as
A', while out of the plane bands are assigned as A". Thus, the 153 normal modes of
vibrations of fentanyl are distributed as Гvib= 105A' + 47A". The theoretical frequencies
and infrared intensities of fentanyl calculated at the B3LYP/6-311++G(d,p) and M06/6-
311++G(d,p) levels are presented in Table S1 of Supporting Information. As expected, in
all cases, the calculated harmonic frequencies are overestimated relative to experiment.
This is mainly due to the harmonic approximation and may be due to the incomplete
treatment of electron correlation in these calculations. Thus, to aid comparison between
the theoretical and experimental frequencies, a scaling factor was used for the calculated
frequencies [21]. As follows from this comparison, both the B3LYP and M06 methods
provide good overall agreement with experiment. As Figure 5 indicates, almost a linear
correlation is found between the experimental and calculated stretching frequencies of
fentanyl at both M06 and B3LYP levels. Nevertheless, the careful examination of the
results in Table S1 indicates that the calculated frequencies with the B3LYP method are
closer to experimental values than those obtained by the M06 method. Besides, most of
the frequencies calculated by the M06 method are larger than those of B3LYP ones, an
observation reported previously for other related systems [22-25].
< Figure 4>
< Figure 5>
4.2.1. C–H vibrations
The C–H stretching vibration in alkanes and aromatic structures are in the regions of
2850–3000 cm-1 and 3000–3100cm-1, respectively [26, 27]. The FT-IR bands for the C–H
stretching vibrations are observed at 3057 cm-1. The calculated C–H stretching vibration
appears at 3054.63 cm-1 at the B3LYP/6-311++G(d,p) level which is in good agreement with
the experimental data (3057 cm-1). The calculated C–H stretching vibrations appear at 2966
cm-1 by the M06/6-311++G(d,p) method.
As evidenced by the PED, this mode (mode no. 9) involves the contribution of 98%.
4.2.2. C=O vibrations
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The C=O bond in esters is assigned in the region of 1730-1750 cm-1 [27]. In this structure,
the C=O stretching vibration is seen at 1656 cm-1. The calculated C=O stretching vibration
appears at 1656.65 cm-1 using the B3LYP/6-311++G (d,p) level which is closer to the
corresponding experimental data (1656 cm-1). However, the M06 method gives a relatively
larger deviation (17 cm-1) from the experimental value. Helios et al. [28] have reported a
similar effect for the B3LYP-and M06-calculated vibration stretching frequency of the
carbonyl group in a polymeric Cu(II)–orotate complex. This is most likely due to the fact that
the M06 functional usually overestimates the strength of the C=O bond, which leads to a
shorter C=O bond length relative to those of B3LYP method and the predicted C=O
stretching frequency is thus larger than experimental. We note, however, that Scuseria [29]
and co-workers have attributed this behavior to the relatively larger percentage of Hartree–
Fock exchange energy in the M06 functional (20%) than in the B3LYP (20%).
This mode (mode no. 29) involves the contribution of 83%, as indicated by the PED.
4.2.3. C–N vibrations
The C-N stretching absorption of amines occurs in the region of 1000-1250 cm-1 [27]. In
this structure, the C-N bond is observed at 1244 cm-1.
The calculated C-N stretching vibration appears at 1228.44 cm-1 using the B3LYP/6-
311++G(d,p) level which was in good agreement with the experimental value. The calculated
C-N stretching vibration appears at 1199.85 cm-1 at the M06/6-311++G(d,p) level.
As indicated by the PED, this mode (mode no. 66) involves the contribution of 12%.
4.3. Chemical shift analysis
Figure 6 shows the experimental 1H NMR spectra of fentanyl. Theoretical simulation of
1H chemical shifts were performed by the GaussView software which is shown in Figure S1.
1
Table 5 lists the experimental and theoretical chemical shifts of H nuclei in fentanyl. It is
1
found that the H chemical shifts (with respect to TMS) occur at 0.58–7.71 and 1.33–8.60
ppm at the B3LYP and M06 levels, respectively, whereas the experimental shifts are in the
range of 1.03–7.42 ppm. The methyl protons (H33-H35) experimentally resonate at 1.03–
1.06 ppm as a multiplet which these chemical shifts are theoretically predicted in the range of
0.58–1.24 ppm and 1.33–2.00 at the B3LYP and M06 levels, respectively. The signal in the
range of 1.93−3.05 ppm is assigned to methylene protons (H37-H48 and H31, H32). The H36
proton of the title compound experimentally shows a multiplet at 4.71 ppm. This chemical
shift theoretically occurs at 3.42 and 4.02 ppm at the B3LYP and M06 levels of theory,
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respectively. The multiplet at 7.10−7.42 ppm corresponds to the aromatic protons (H26-30,
H49-53) that are calculated at 7.30−7.71 and 7.95−8.60 ppm by B3LYP and M06,
respectively. As Figure 7 indicates, H36 and H44 atoms indicate the largest δexp-δcal value at
both B3LYP and M06 levels. More especially, the average absolute standard deviation of the
calculated 1H NMR chemical shifts is calculated to be 0.44 and 0.79 at the B3LYP and M06
levels.
<Figure 6>
<Table 5>
< Figure 7>
The 13C chemical shifts (with respect to TMS) are assigned in the range of 10.93−178.92
and 10.62−183.00 ppm by B3LYP and M06 methods, respectively, while the corresponding
experimental data are observed in the range of 9.58−173.5 ppm (Figure 6 and Table 6). The
largest deviation between the calculated and experimental 13C NMR chemical shifts (δexp-δcal)
is seen for C19 with -8.51 and -8.23 ppm at the B3LYP and M06 levels, respectively. The
chemical shifts of C11, C17, C13 and C10 atoms are experimentally located at 9.58, 22.57,
28.49 and 30.56 ppm, respectively. The theoretical chemical shifts of these atoms are
assigned at 10.93 (error approx. -1.35 ppm), 28.04 (error approx. -5.47 ppm), 31.11 (error
approx. -2.62 ppm) and 34.25 (error approx. -3.69 ppm) at the B3LYP, and 10.62 (error
approx. -1.04 ppm), 27.95 (error approx. -5.38 ppm), 28.08 ppm (error approx. 0.41 ppm) and
33.07 ppm (error approx. -2.51 ppm) at the M06 level. As Figure 7 indicates, the largest
13
deviation of the calculated C chemical shifts from the experimental values is seen for the
C20 and C8 atoms. Besides, the average absolute standard deviation of 13C chemical shifts is
5.2 and 5.5 at the B3LYP and M06 levels, respectively. This clearly indicates the larger
deviation of 13C chemical shifts from the experimental data than those of 1H chemical shifts.
<Table 6>
1
13
The relationship between the experimental and computed chemical shifts of H and C
NMR is shown in Figure 8. As evident, the correlation between the experimental and
calculated chemical shifts is better for 13C atoms than for 1H atoms. This discrepancy can be
expected since the 1H chemical shifts were more sensitive to solvent effects [30]. As seen in
Figure 8, the squared correlation coefficients (R2) values obtained at the B3LYP level are
slightly larger than those of at the M06 level. This indicates that for the system under study,
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the B3LYP provides more reliable 13C chemical shifts than the M06, may be due to the
proper description of the structure of this molecule by the former density functional.
<Figure 8>
4.4. Frontier molecular orbital analysis
Density of states (DOS) diagram was obtained from the molecular orbital data and
plotted by the GaussSum program [16]. The DOS diagram of fentanyl is shown in Figure 9. It
is well-known that chemical stability of a molecule is largely affected by the frontier orbitals
[31]. The highest occupied molecular orbital (HOMO) represents electron-donating
capability, while the lowest unoccupied molecular orbital (LUMO) represents electron
accepting capability. Thus, it is expected that the energy difference between the HOMO and
LUMO (HOMO-LUMO energy gap) shows the chemical activity of the molecule. The
calculated HOMO-LUMO energy gap of the title compound is 5.43 and 6.1 eV at the B3LYP
and M06 levels, respectively. Hence, a relatively less kinetic stability is predicted for this
molecule at the B3LYP level. Note that the relatively larger energy gap between the HOMO
and LUMO of fentanyl at the M06 level compared to the B3LYP can be related to the large
destabilization of the LUMO (Figure 9).
<Figure 9>
4.5. MEP analysis
The MEP analysis can be regarded as a powerful tool for identifying the possible
interaction sites around a molecule [32-34]. Positive area of the MEP is indicative of a
nucleophilic site, while negative region is associated with an electrophilic site. The MEP map
of fentanyl is shown in Figure 10. One can see that the most negative region on the MEP map
of fentanyl is associated with the lone-pairs of the oxygen atom with a value of -42 kcal/mol.
This indicates that the oxygen atom of this molecule is the most reactive site to interact
favorably with an acidic reagent in the protonation reaction. On the other hand, the MEP of
fentanyl shows the presence of positive regions around the hydrogen atoms of phenyl groups,
which clearly indicates the propensity of these sites for the formation of intermolecular
interactions with potential electron-rich sites.
<Figure 10>
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5. Conclusion
The title compound, fentanyl, was synthesized via one-pot reactions of 4-
piperidonemonohydrochloride, phenylacetaldehyde, sodiumtriacetoxyborohydride, propionyl
chloride. The structure of fentanyl was determined and characterized by elemental analysis,
1
FT-IR, H and 13C NMR. The comparison between the calculated and experimental values
indicated that the B3LYP/6-311++G(d,p) can predict the bond lengths, bond angles and
dihedral angles of fentanyl better than the M06/6-311++G(d,p) method. In addition, it is
found that the B3LYP calculated vibrational frequencies are in good agreement with the
experimental FT-IR spectra. The MEP map of fentanyl predicts that the oxygen atom of
fentanyl is the most reactive site to an electrophilic attack.
Acknowledgments
This work was supported by the Sandoogh Hemayate az Pajuoheshgharane Keshvare Iran.
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1987.
[27] R.M. Silverstein, G.C. Basseler and T.C. Morill, Spectrometric Identification of
Organic Compounds, 4th ed. New York: John Wiley and Sons, 1981. QD272.S6 S55.
[28] K. Helios, R. Wysokínski, A. Pietraszko, D. Michalska, Vib. Spectrosc. 55 (2011) 207.
[29] C.A. Jiménez-Hoyos, B.G. Janesko and G.E. Scuseria, Phys. Chem. Chem. Phys. 10
(2008) 6621.
[30] G.K. Hamer, I.R. Peat, W.F. Reynolds, Can. J. Chem. 51 (1973) 897.
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Spectrosc. 77 (2010) 612.
[32] P. Politzer, D.G. Truhlar (Eds.), Chemical Application of Atomic and Molecular
Electrostatic Potentials, Plenum, New York, 1981.
[33] M.D. Esrafili, Comput. Theor. Chem. 1015 (2013) 1.
[34] M.D. Esrafili, F. Mohammadian-Sabet, Chem. Phys. Lett. 628 (2015) 71.
12

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Table 1. The experimental (Exp.) and calculated bond lengths (Å) of fentanyl at different
levels of theory
B3LYP/6-
311++G(d,p)
1.39
B3LYP/6-
311+G(d)
1.39
M06/6-
311++G(d,p)
1.38
M06/6-
311+G(d)
1.38
1.38
1.39
1.38
1.38
1.49
1.52
1.44
1.45
1.52
1.53
1.52
1.52
1.47
1.42
1.37
1.39
1.38
1.39
1.21
1.51
1.51
Bond length
Exp.
C23-C24
C24-C25
C25-C20
C22-C23
C21-C22
C20-C19
C19-C18
C18-N15
N15-C14
C14-C13
C13-C12
C12-C17
C17-C16
C12-N7
N7-C1
1.39(1)
1.39(1)
1.40(1)
1.39(1)
1.39(1)
1.51(1)
1.54(1)
1.46(1)
1.46(2)
1.52(2)
1.54(2)
1.54(2)
1.54(2)
1.48(2)
1.44(2)
1.36(2)
1.39(2)
1.39(2)
1.38(2)
1.22(2)
1.51(2)
1.49(2)
1.39
1.39
1.38
1.40
1.40
1.39
1.39
1.39
1.38
1.39
1.39
1.38
1.51
1.51
1.50
1.54
1.53
1.52
1.45
1.45
1.44
1.46
1.46
1.45
1.53
1.53
1.52
1.54
1.54
1.53
1.53
1.53
1.52
1.54
1.54
1.52
1.48
1.48
1.47
1.43
1.43
1.42
N7-C8
1.37
1.37
1.37
C1-C6
1.39
1.39
1.39
C6-C5
1.39
1.39
1.38
C1-C2
1.39
1.39
1.39
C8-O9
1.22
1.22
1.21
C8-C10
C10-C11
1.52
1.52
1.51
1.52
1.52
1.51
(1): N-(2-phenylethyl) nitroaniline [18].
(2): (1R)-2-[(3R,4S)-3-Methyl-4-(N-phenyl-N-propionylamino)piperidin-1-yl]-1-phenylethyl p-bromobenzoate and N-
{(3R,4S)-1-[(2S)-2-(4-bromophenyl)-2-hydroxyethyl]-3-methyl-piperidin-4-yl}-N-phenylacrylamide [19]
.
1

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Table 2. The experimental (Exp.) and calculated bond angles (°) of fentanyl at different
levels of theory
B3LYP/6-
311++G(d,p)
111.9
B3LYP/6-
311+G(d)
111.9
M06/6-
311++G(d,p)
110.8
M06/6-
311+G(d)
110.8
113.4
112.0
109.7
110.4
110.2
116.2
121.0
121.9
112.4
121.8
122.6
Bond angle
Exp.
C20-C19-C18 111.0(1)
C19-C18-N15 112.6(1)
N15-C16-C17 110.7(2)
C16-C17-C12 110.0(2)
C17-C12-C13 110.4(2)
C12-C13-C14 108.2(2)
113.2
113.3
113.4
110.1
112.2
111.9
110.6
110.1
109.7
110.3
110.2
110.5
110.6
110.7
110.1
C12-N7-C1
C12-N7-C8
N7-C8-O9
C8-C10-C11
O9-C8-C10
C1-N7-C8
111.6(2)
117.1(2)
122.1(2)
112.2(2)
121.7(2)
122.0(2)
116.5
116.5
116.1
120.9
120.9
121.0
121.5
121.6
121.8
112.4
112.4
112.3
121.3
121.3
121.8
122.4
122.4
122.7
(1): N-(2-phenylethyl) nitroaniline [18].
(2): (1R)-2-[(3R,4S)-3-Methyl-4-(N-phenyl-N-propionylamino)piperidin-1-yl]-1-phenylethyl p-bromobenzoate and N-
{(3R,4S)-1-[(2S)-2-(4-bromophenyl)-2-hydroxyethyl]-3-methyl-piperidin-4-yl}-N-phenylacrylamide [19].
2

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Table 3. The experimental (Exp.) and calculated dihedral angles (°) of fentanyl at different
levels of theory
Dihedral
B3LYP/ 6-
311++G(d,p)
-62.1
B3LYP/6-
311+G(d)
-62.1
M06/6-
M06/6-
Exp.
angle
311++G(d,p) 311+G(d)
C16-C17-C12-C13
C18-N15-C14-C13
C12-N7-C1-C2
C16-C17-C12-C13
C17-C12-C13-C14
C12-C13-C14-N15
C18-N15-C14-C13
C17-C12-N7-C8
C17-C12-N7-C1
C12-N7-C8-O9
C12-N7- C1-C2
-54.4(1)
167.9(1)
-96.3(1)
-54.5(2)
-54.9 (2)
58.9(2)
167.9(2)
157.9(2)
-14.2(2)
4.4(2)
-62.8
163.2
-80.6
-62.8
28.9
-62.7
163.6
-80.6
-62.7
28.4
162.0
162.5
-80.8
-80.7
-62.1
-62.1
28.4
28.2
34.3
34.5
34.5
34.9
162.0
162.4
63.0
163.2
62.5
163.5
62.7
62.9
-115.9
-0.8
-115.9
-1.0
-114.5
-0.1
-114.5
-0.3
-96.3(2)
-80.7
-80.7
-80.6
-80.5
(1): 4-{N-[2-(1,3-Dioxo-1,3-dihydroisoindol-2-yl)-3-phenylpropionyl]anilino}-1-phenethylpiperidinium chloride
methanol.disolvate [20].
(2): (1R)-2-[(3R,4S)-3-Methyl-4-(N-phenyl-N-propionylamino)piperidin-1-yl]-1-phenylethyl p-bromobenzoate and N-
{(3R,4S)-1-[(2S)-2-(4-bromophenyl)-2-hydroxyethyl]-3-methyl-piperidin-4-yl}-N-phenylacrylamide [19].
3

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Table 4. Calculated Mullikan atomic charges (e) of fentanyl
B3LYP/6-
311++G(d,p)
1.047
B3LYP/6-
311+G(d)
1.495
M06/6-
311++G(d,p)
0.740
M06/6-
311+G(d)
1.153
atom
C20
C19
C18
N15
C16
C17
C12
C13
C14
N7
-0.534
-0.682
0.277
-1.074
-0.800
0.525
-0.671
-0.220
-0.006
-0.051
-0.047
-1.570
0.412
-1.045
-0.664
0.275
-0.298
-0.337
-0.853
0.106
-0.722
-0.576
-1.023
-0.015
-0.783
0.861
-0.524
-0.298
1.675
0.091
-0.468
0.816
-0.275
0.439
-0.711
0.452
C1
-0.432
-0.062
-0.211
-0.225
-0.638
-0.406
0.074
-0.216
-0.057
-0.217
-0.159
-0.518
0.204
C8
0.090
O9
-0.276
-0.331
-1.057
-0.274
-0.383
-1.050
C10
C11
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Table 5. Calculated (δcal) and experimental (δexp) 1H chemical shifts of fentanyl
Calculated
Atom
δexp
B3LYP/6-
311++G(d,p)
0.58
0.88
1.24
1.61
1.62
1.89
2.27
2.28
2.31
2.43
2.50
2.56
2.76
2.88
2.93
3.18
3.42
3.50
7.30
7.33
7.37
7.42
7.42
7.48
7.48
7.50
7.55
M06/6-
311++G(d,p)
1.33
δexp-δB3LYP
δexp-δM06
H33
H34
H35
H32
H43
H31
H45
H38
H41
H40
H46
H47
H48
H37
H39
H42
H36
H44
H49
H50
H51
H53
H30
H52
H26
H29
H28
H27
0.45
0.16
-0.18
0.32
-0.30
-0.72
-0.94
-0.49
-0.24
-1.00
-1.04
0.12
-0.59
-0.39
-1.14
-0.77
-0.73
-0.70
-0.71
-0.66
0.70
-2.82
-0.95
-1.20
-0.81
-0.87
-0.84
-0.83
-0.91
-1.06
-0.65
-1.18
1.03 -1.06
1.76
2.00
2.42
2.22
2.47
2.87
2.91
2.77
2.95
2.99
3.00
3.48
3.29
3.49
3.71
4.02
4.31
8.05
8.31
7.95
8.05
8.04
8.08
8.16
-
-
1.93-1.98
0.36
-0.42
-0.44
0.75
-0.13
0.13
1.47 – 1.49
1.85 – 1.83
2.23 – 2.18
2.59 – 2.56
2.78 – 2.75
-0.65
-0.33
-0.01
-0.29
-0.15
-0.13
1.30
-2.01
-0.20
-0.22
-0.23
-0.24
-0.22
-0.23
-0.23
0.45
3.05 – 3.03
4.71
3.05 – 3.03
7.10- 7.42
-
-
-
-
-
-
-
-
-
8.34
7.95
8.6
0.16
-0.18
7.71
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Table 6. Calculated (δcal) and experimental (δexp) 13C NMR chemical shifts of fentanyl
Calculated
Atom
δexp
B3LYP/6-
311++G(d,p)
M06/6-
311++G(d,p)
δexp-δB3LYP
δexp-δM06
C11
C17
C13
C10
C19
C16
C14
C12
C18
C23
C4
10.93
-1.35
-5.47
-2.62
-3.69
-8.51
-4.41
-3.95
-5.4
-
10.62
-1.04
-5.38
0.41
-2.51
-8.23
-3.2
-2.46
-5.67
-
9.58
22.57
28.49
30.56
33.82
52.14
53.08
60.46
-
28.04
27.95
31.11
28.08
34.25
33.07
42.33
42.05
56.55
55.34
57.03
55.54
65.86
66.13
69.20
70.98
131.89
133.91
134.39
135.02
135.93
136.03
135.09
135.76
136.19
137.24
149.95
155.97
178.92
-5.91
-5.7
-6.05
-6.43
-6.69
-5.62
-
134
-8.02
-6.97
-7.97
-7.56
-7.76
-7.61
-
125.98
128.21
128.34
128.59
129.24
130.41
-
135.18
136.31
136.15
137.00
138.02
140.00
137.23
138.23
138.50
149.29
155.82
183.00
C22
C24
C21
C2
C25
C5
-
-
-
C6
-
-
-
C3
1.61
-9.71
-
0.35
-9.05
-
138.85
140.24
-
C20
C1
C8
-5.42
-9.5
173.5
†
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Scheme 1. One pot synthesis of fentanyl via reductive alkylation and amination reaction in
the presence of sodium triacetoxyborohydride (STAB)
1

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Figure 1.The optimized structure of fentanyl
2

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Figure 2. Linear correlations between the experimental and calculated bond lengths of
fentanyl
3

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Figure 3. Atomic Mulliken charges and orientation of the dipole moment of fentanyl
calculated at the B3LYP/6-31++G(d,p) level
4

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Experimental
Frequency (cm-1)
B3LYP/6-311++G(d,p)
M06/6-311++G(d,p)
Figure 4. The experimental and calculated IR spectra of fentanyl
5

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Figure 5. Relationship between the experimental and calculated frequencies of fentanyl
6

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Figure 6. Experimental 1H (left) and 13C (right) chemical shifts of fentanyl
7

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Figure 7. The deviation of calculated 1H (above) and 13C (below) chemical shifts from the
corresponding experimental values
8

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Figure 8. Correlation between the experimental and calculated 1H and 13C chemical shifts of
fentanyl
9

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B3LYP/6-311++G (d,p)
5.43
M06/6-311++G (d,p)
6.1
Figure 9. DOS diagram, HOMO (left) and LUMO (right) of fentanyl
10

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Figure 10. The molecular electrostatic potential (MEP) of fentanyl. The color range, in
kcal/mol, is: red > 4.5, 4.5 > yellow > -11.0, -11.0 > green > -26.6 and blue < -26.6.
11