# Quantum Calculation for Musk Molecules Infrared Spectra towards the Understanding of Odor

Authors: Elaine Rose Maia; Daniela Regina Bazuchi Magalhães; Dan A. Lerner; Dorothée Berthomieu; Jean-Marie Bernassau
Journal: Advances in Chemistry
 (2014)

---

## Abstract

It is not clear so far how humans can recognize odor. One of the theories regarding structure-odor relationship is vibrational theory, which claims that odors can be recognized by their modes of vibration. In this sense, this paper brings a novel comparison made between musky and nonmusky molecules, as to check the existence of correlation between their modes on the infrared spectra and odor. For this purpose, sixteen musky odorants were chosen, as well as seven other molecules that are structurally similar to them, but with no musk odor. All of them were submitted to solid theoretical methodology (using molecular mechanics/molecular dynamics and Neglect of Diatomic Differential Overlap Austin Model 1 methods to optimize geometries) as to achieve density functional theory spectra information, with both Gradient Corrected Functional Perdew-Wang generalized-gradient approximation (GGA/PW91) and hybrid Becke, three-parameter, Lee-Yang-Parr (B3LYP) functional. For a proper analysis over spectral data, a mathematical method was designed, generating weighted averages for theoretical frequencies and computing deviations from these averages. It was then devised that musky odorants satisfied demands of the vibrational theory, while nonmusk compounds belonging either to nitro group or to acyclic group failed to fulfill the same criteria.


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## Body

## 1. Introduction

### 1.1. Theories regarding Odor Prediction and Recognition

Musks are responsible for bringing sensuality and warmth to a fragrance [1], as well as adding their excellent fixative properties [2, 3]. Presently, natural products extraction involves high costs and generates small amounts of raw material, so synthetic odorants are greatly demanded. To properly design a new odorant, previous information on how odors are read is necessary. There are major recent advances on neurobiology, biophysics, biochemical fields [4–7], though it is still unclear how humans recognize odor. At this scenario, quantitative structure-activity relationship models (QSAR models) are valuable for the proposal of new potential musky smelling molecules [8–12]. Such approach allows for the reduction in the number of costly and unnecessary chemical syntheses. Theories regarding odor recognition at the biological level have also been discussed in the literature. One of them, known as the odotope theory [13–15], states that noncovalent bonds (i.e., weak repulsive and attractive interactions) between the molecule and the olfactory receptor (OR) proteins (responsible for decoding the molecule and starting transduction) would elicit a unique response in the cerebral cortex.A second theory regarding structure-odor relationship is the vibrational theory, which relates the molecule’s vibrational modes to its odor. It was firstly proposed by Dyson in 1938, followed by Wright, in 1977, and refined by several authors [16]. It claims that ORs would be able to recognize odorant vibrational modes. In 1996 [17], Turin suggested that such reading would occur, at the protein-odorant level, through a mechanism close to inelastic electron tunneling spectroscopy (IETS), an inelastic nonoptical vibrational spectroscopy [18]. After building a specific algorithm to mimic vibrational modes at protein level, the author could state thatmusks—for instance—will present four bands near 700, 1000, 1500 (or 1750 cm−1 for nitromusks), and 2200 cm−1, and that each band will have 400 cm−1 width [19]. There is much to be understood concerning odor recognition, supported on vibrational theory’s ideas, as indicated by the variety of papers dealing with the subject [20–24].


### 1.2. Paper’s Aims

In order to explore vibrational theory, musks and non-musks (see Figure1) have been equally modeled so to come to their theoretical IR spectra. Firstly molecules have been computationally analyzed by molecular mechanics and molecular dynamics (MM/MD), in order to ascertain the conformational space available to them. After, semiempirical calculations employing Neglect of Diatomic Differential Overlap Austin Model 1 (NDDO AM1), Hamiltonian took place for geometry corrections. Then final calculations for energy optimization and IR spectra collection were set with density functional theory (DFT), using both Gradient Corrected Functional Perdew-Wang generalized-gradient approximation (GGA/PW91) and hybrid Becke, three-parameter, Lee-Yang-Parr (B3LYP) functionals, with the double numerical basis set with polarization (DNP) for GGA/PW91 and 6-311+G(d,p) for B3LYP. Methodology adopted is up-to-date with the literature and was mainly based on Lerner and coworkers paper [26]. For a complete discussion on computed harmonic vibrational frequencies and their scaling factors and accuracy, see data obtained by Scott and Radom [27].Figure 1
Odorants under study: macrocyclic musks (MCM): pentadecanolide (1), (R)-exaltolide (2), (S)-exaltolide (3),cis-globanone (4), andtrans-globanone (5); polycyclic musks (PCM): (4S,7S)-galaxolide (6), (4S,7R)-galaxolide (7), indane (8), tetralin (9), and tonkene (10); nitromusks (NM): musk ketone (11), musk moskene (12), and musk ambrette (13); acyclic musks (ACM): romandolide (14), helvetolide (15), and cyclomusk (16); nonmusks: macrocyclic analogs (MCa) (17) and (18), acyclic analogs (Aa) (19) and (20), and nitro analogs (Na) (21), (22), and (23).GGA/PW91 and B3LYP theoretical spectra were compared to the experimental data (when available in free data banks as NIST and SDBS) and then were evaluated concerning the expression of the four characteristic musk bands (centered at 700, 1000, 1500 or 1750, and 2200 cm−1). Now, these four bands were properly indicated using a specific algorithm built to reproduce IETS at biological level; however, the vibrational modes primarily responsible for such bands were not nominated. To clarify this question, a comparison was carried between IR theoretical data and IET data published previously, since both spectra show the same vibrational modes at the same frequencies, and it is much simpler to estimate theoretical IR spectra. Aside from the equivalence on estimating vibrational modes, there are no other comparisons that could fit in, once mode intensities are differently calculated in one technique and another, generating bands that can be either more prominent or even absent when comparing spectra. Besides, using IR spectra to predict odor or olfactory receptor affinity has failed repeatedly [28]. Finally, vibrational modes responsible for “musk bands” in the spectra are not to be taken as solely responsible for musk odor. It is well known that there are several molecular descriptors involved at major biological phenomena, such as carrying the odorant from the environment to an OR and docking odorant-OR, and they are equally relevant when considering the vibrationally assisted odor recognition mechanism.The sixteen musks1–16 are already in use in perfumes, so to have their activity is certified. The seven molecules17–23 are structurally similar to the previous molecules but do not possess any musky odor; besides, nonmusks17 and18 arewoody. Absence of odor is not to be taken as a different odor character but (i) as a molecule’s inability to bind its OR, due to particularities of its structure, or (ii) as the lack of specific vibrational modes in their minimum quantity, precluding proper energy decrease on electron scattering and its subsequent tunneling [13, 14, 16]. So, regarding adopted criteria relying on the choice of such molecules, it addresses the main hypothesis here being tested: only musk odorants are supposed to express vibrational modes under mentioned ranges, and no other molecule is supposed to present the same vibrational pattern. All compounds have their IUPAC name and Chemical Abstracts Service (CAS) registry number listed in Table 1.Table 1
Molecules studied.
Number
IUPAC name
CAS number
1
Oxacyclohexadecan-2-one
106-02-5
2
16(R)-Methyl-oxacyclohexadecan-2-one
69297-56-9
3
16(S)-Methyl-oxacyclohexadecan-2-one
129214-00-2
4
(5Z)-Cyclohexadec-5-en-1-one
37609-25-9
5
(5E)-Cyclohexadec-5-en-1-one
6
(4S,7S)-Cyclopenta[g]-2-benzopyran, 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethyl
172339-62-7
7
(4S,7R)-Cyclopenta[g]-2-benzopyran, 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethyl
252332-95-9
8
1-(2,3-Dihydro-1,1,2,3,3-pentamethyl-1H-inden-5-yl)-ethanone
4755-83-3
9
1-[(6S)-5,6,7,8-Tetrahydro-3,5,5,6,8,8-hexamethyl-2-naphthalenyl]-ethanone
85549-79-7
10
2H-[1]-Benzothieno[3,2-b]pyran-2-one
5732-22-9
11
4-(1,1-Dimethylethyl)-2,6-dimethyl-3,5-dinitro-benzaldehyde
99758-50-6
12
4-(1,1-Dimethylethyl)-2,6-dimethyl-3,5-dinitro-benzaldehyde
116-66-5
13
none
14
2-(1-Oxopropoxy)-, 1-(3,3-dimethylcyclohexyl)ethyl ester
236391-76-7
15
1-Propanol, 2-[1-(3,3-dimethylcyclohexyl)ethoxy]-2-methyl-, 1-propanoate
141773-73-1
16
1-Cyclopentene-1-propanol,β,β,2-trimethyl-5-(1-methylethenyl)-, 1-propanoate
84012-64-6
17
Oxacyclotetradecane-2,10-dione
38223-27-7
18
Cyclotetradecanone
3603-99-4
19
2-(1-Oxopropoxy)-, 1-cyclohexyl-1-methylethyl ester
610770-00-8
20
none
21
2-Methoxy-1-methyl-4-(2-methyl-2-propanyl)-3,5-dinitrobenzene
99758-79-9
22
2-Methoxy-4-methyl-1-(2-methylpropyl)-3,5-dinitro-benzene
99758-78-8
23
2,4-Bis(1,1-dimethylethyl)-5-methoxy-3-nitro-benzaldehyde
107342-73-4


## 1.1. Theories regarding Odor Prediction and Recognition

Musks are responsible for bringing sensuality and warmth to a fragrance [1], as well as adding their excellent fixative properties [2, 3]. Presently, natural products extraction involves high costs and generates small amounts of raw material, so synthetic odorants are greatly demanded. To properly design a new odorant, previous information on how odors are read is necessary. There are major recent advances on neurobiology, biophysics, biochemical fields [4–7], though it is still unclear how humans recognize odor. At this scenario, quantitative structure-activity relationship models (QSAR models) are valuable for the proposal of new potential musky smelling molecules [8–12]. Such approach allows for the reduction in the number of costly and unnecessary chemical syntheses. Theories regarding odor recognition at the biological level have also been discussed in the literature. One of them, known as the odotope theory [13–15], states that noncovalent bonds (i.e., weak repulsive and attractive interactions) between the molecule and the olfactory receptor (OR) proteins (responsible for decoding the molecule and starting transduction) would elicit a unique response in the cerebral cortex.A second theory regarding structure-odor relationship is the vibrational theory, which relates the molecule’s vibrational modes to its odor. It was firstly proposed by Dyson in 1938, followed by Wright, in 1977, and refined by several authors [16]. It claims that ORs would be able to recognize odorant vibrational modes. In 1996 [17], Turin suggested that such reading would occur, at the protein-odorant level, through a mechanism close to inelastic electron tunneling spectroscopy (IETS), an inelastic nonoptical vibrational spectroscopy [18]. After building a specific algorithm to mimic vibrational modes at protein level, the author could state thatmusks—for instance—will present four bands near 700, 1000, 1500 (or 1750 cm−1 for nitromusks), and 2200 cm−1, and that each band will have 400 cm−1 width [19]. There is much to be understood concerning odor recognition, supported on vibrational theory’s ideas, as indicated by the variety of papers dealing with the subject [20–24].


## 1.2. Paper’s Aims

In order to explore vibrational theory, musks and non-musks (see Figure1) have been equally modeled so to come to their theoretical IR spectra. Firstly molecules have been computationally analyzed by molecular mechanics and molecular dynamics (MM/MD), in order to ascertain the conformational space available to them. After, semiempirical calculations employing Neglect of Diatomic Differential Overlap Austin Model 1 (NDDO AM1), Hamiltonian took place for geometry corrections. Then final calculations for energy optimization and IR spectra collection were set with density functional theory (DFT), using both Gradient Corrected Functional Perdew-Wang generalized-gradient approximation (GGA/PW91) and hybrid Becke, three-parameter, Lee-Yang-Parr (B3LYP) functionals, with the double numerical basis set with polarization (DNP) for GGA/PW91 and 6-311+G(d,p) for B3LYP. Methodology adopted is up-to-date with the literature and was mainly based on Lerner and coworkers paper [26]. For a complete discussion on computed harmonic vibrational frequencies and their scaling factors and accuracy, see data obtained by Scott and Radom [27].Figure 1
Odorants under study: macrocyclic musks (MCM): pentadecanolide (1), (R)-exaltolide (2), (S)-exaltolide (3),cis-globanone (4), andtrans-globanone (5); polycyclic musks (PCM): (4S,7S)-galaxolide (6), (4S,7R)-galaxolide (7), indane (8), tetralin (9), and tonkene (10); nitromusks (NM): musk ketone (11), musk moskene (12), and musk ambrette (13); acyclic musks (ACM): romandolide (14), helvetolide (15), and cyclomusk (16); nonmusks: macrocyclic analogs (MCa) (17) and (18), acyclic analogs (Aa) (19) and (20), and nitro analogs (Na) (21), (22), and (23).GGA/PW91 and B3LYP theoretical spectra were compared to the experimental data (when available in free data banks as NIST and SDBS) and then were evaluated concerning the expression of the four characteristic musk bands (centered at 700, 1000, 1500 or 1750, and 2200 cm−1). Now, these four bands were properly indicated using a specific algorithm built to reproduce IETS at biological level; however, the vibrational modes primarily responsible for such bands were not nominated. To clarify this question, a comparison was carried between IR theoretical data and IET data published previously, since both spectra show the same vibrational modes at the same frequencies, and it is much simpler to estimate theoretical IR spectra. Aside from the equivalence on estimating vibrational modes, there are no other comparisons that could fit in, once mode intensities are differently calculated in one technique and another, generating bands that can be either more prominent or even absent when comparing spectra. Besides, using IR spectra to predict odor or olfactory receptor affinity has failed repeatedly [28]. Finally, vibrational modes responsible for “musk bands” in the spectra are not to be taken as solely responsible for musk odor. It is well known that there are several molecular descriptors involved at major biological phenomena, such as carrying the odorant from the environment to an OR and docking odorant-OR, and they are equally relevant when considering the vibrationally assisted odor recognition mechanism.The sixteen musks1–16 are already in use in perfumes, so to have their activity is certified. The seven molecules17–23 are structurally similar to the previous molecules but do not possess any musky odor; besides, nonmusks17 and18 arewoody. Absence of odor is not to be taken as a different odor character but (i) as a molecule’s inability to bind its OR, due to particularities of its structure, or (ii) as the lack of specific vibrational modes in their minimum quantity, precluding proper energy decrease on electron scattering and its subsequent tunneling [13, 14, 16]. So, regarding adopted criteria relying on the choice of such molecules, it addresses the main hypothesis here being tested: only musk odorants are supposed to express vibrational modes under mentioned ranges, and no other molecule is supposed to present the same vibrational pattern. All compounds have their IUPAC name and Chemical Abstracts Service (CAS) registry number listed in Table 1.Table 1
Molecules studied.
Number
IUPAC name
CAS number
1
Oxacyclohexadecan-2-one
106-02-5
2
16(R)-Methyl-oxacyclohexadecan-2-one
69297-56-9
3
16(S)-Methyl-oxacyclohexadecan-2-one
129214-00-2
4
(5Z)-Cyclohexadec-5-en-1-one
37609-25-9
5
(5E)-Cyclohexadec-5-en-1-one
6
(4S,7S)-Cyclopenta[g]-2-benzopyran, 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethyl
172339-62-7
7
(4S,7R)-Cyclopenta[g]-2-benzopyran, 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethyl
252332-95-9
8
1-(2,3-Dihydro-1,1,2,3,3-pentamethyl-1H-inden-5-yl)-ethanone
4755-83-3
9
1-[(6S)-5,6,7,8-Tetrahydro-3,5,5,6,8,8-hexamethyl-2-naphthalenyl]-ethanone
85549-79-7
10
2H-[1]-Benzothieno[3,2-b]pyran-2-one
5732-22-9
11
4-(1,1-Dimethylethyl)-2,6-dimethyl-3,5-dinitro-benzaldehyde
99758-50-6
12
4-(1,1-Dimethylethyl)-2,6-dimethyl-3,5-dinitro-benzaldehyde
116-66-5
13
none
14
2-(1-Oxopropoxy)-, 1-(3,3-dimethylcyclohexyl)ethyl ester
236391-76-7
15
1-Propanol, 2-[1-(3,3-dimethylcyclohexyl)ethoxy]-2-methyl-, 1-propanoate
141773-73-1
16
1-Cyclopentene-1-propanol,β,β,2-trimethyl-5-(1-methylethenyl)-, 1-propanoate
84012-64-6
17
Oxacyclotetradecane-2,10-dione
38223-27-7
18
Cyclotetradecanone
3603-99-4
19
2-(1-Oxopropoxy)-, 1-cyclohexyl-1-methylethyl ester
610770-00-8
20
none
21
2-Methoxy-1-methyl-4-(2-methyl-2-propanyl)-3,5-dinitrobenzene
99758-79-9
22
2-Methoxy-4-methyl-1-(2-methylpropyl)-3,5-dinitro-benzene
99758-78-8
23
2,4-Bis(1,1-dimethylethyl)-5-methoxy-3-nitro-benzaldehyde
107342-73-4


## 2. Methods and Methodology

### 2.1. Computational Methods

Calculation programs used were those available in the Materials Studio Package Program [29] and Gaussian 09 [30] for B3LYP calculations. Molecules had their conformational space studied undervacuum environment through MM/DM calculations, using the CFF99/COMPASS [31] force field implemented in the Discover Simulation program [32, 33]. Main parameters chosen for MM routine were Conjugate Gradient method [34] with the Polak-Ribiere algorithm [35], running until it achieved convergence at 1.0 × 10−4kcal·mol−1·Ǻ−1. MD trajectories were carried out at 650 K, during 1.0 ns, with a time step of 1.0 fs (therefore, collecting 1.000 frames), in the canonical ensemble. After previous scanning in which temperature and trajectory time were changed, parameters chosen showed to be effective on expressing molecules flexibility, allowing the collection of a representative subset of initial conformations.Selected conformers from MM/DM procedure were then minimized with Vamp program [36], using NDDO AM1 [37–39], as a previous optimization step towards DFT calculation. Spin multiplicity was automatically determined, and a convergence of 0.1 kcal·mol−1·Ǻ−1 for the heat of formation value was set. Self-consistent field (SCF) cycles had a convergence tolerance of 5.0 × 10−7eV·atom−1.Final geometries were minimized using the DMol3 program [40–42] for DFT calculations. Basis set chosen was DNP [43], with GGA/PW91 [44] as exchange functional. Total energy convergence of 1.0 × 10−5 Ha was required, with a 3.7 Å global cutoff. Final cutoff of the SCF cycles was 5.0 × 10−7eV·atom−1, and the orbital cutoff quality was kept equal to 0.1 eV·atom−1. The same starting structure used in GGA/PW91 calculation was employed for hybrid functional B3LYP [45] calculation with 6-311+G(d,p) basis set, now using Gaussian 09. Molden’s processing program [46] was applied, along with Xming emulator [47], to achieve IR continuum spectra.


### 2.2. Development of a Frequency-Weighted Average and Other Useful Tools

A mathematical formula had to be developed in this paper, in order to consider each and every mode belonging to the same 400 cm-1 range, as well as their intensities. Therefore, the use of weighted averages over theoretical data was chosen; its numerical result was calledcentral frequency (cf). With this central frequency, it became possible to consider all theoretical peaks occurring in the vicinity of the diagnostic frequencies, instead of just affirming the existence of the expected band only by naming the most intense theoretical peak. Central frequencies were estimated as follows:
(1)
Central
frequency
=
∑
i
=
1
n
ν
i
×
in
t
i
∑
i
=
1
n
in
t
i
.This mathematical approach (which simply generates a frequency-weighted average) was applied to theoretical frequencies found at ±200 cm−1 around 700, 1000, and 1500 (or 1750) cm−1 and resulted in central frequencies for compounds1–23, which were computed in Table 4 (for GGA/PW91 data) and in Table 5 (for B3LYP data). The mentioned range has been chosen so as to enable each band to complete its 400 cm−1 width, as established in the vibrational theory.


## 2.1. Computational Methods

Calculation programs used were those available in the Materials Studio Package Program [29] and Gaussian 09 [30] for B3LYP calculations. Molecules had their conformational space studied undervacuum environment through MM/DM calculations, using the CFF99/COMPASS [31] force field implemented in the Discover Simulation program [32, 33]. Main parameters chosen for MM routine were Conjugate Gradient method [34] with the Polak-Ribiere algorithm [35], running until it achieved convergence at 1.0 × 10−4kcal·mol−1·Ǻ−1. MD trajectories were carried out at 650 K, during 1.0 ns, with a time step of 1.0 fs (therefore, collecting 1.000 frames), in the canonical ensemble. After previous scanning in which temperature and trajectory time were changed, parameters chosen showed to be effective on expressing molecules flexibility, allowing the collection of a representative subset of initial conformations.Selected conformers from MM/DM procedure were then minimized with Vamp program [36], using NDDO AM1 [37–39], as a previous optimization step towards DFT calculation. Spin multiplicity was automatically determined, and a convergence of 0.1 kcal·mol−1·Ǻ−1 for the heat of formation value was set. Self-consistent field (SCF) cycles had a convergence tolerance of 5.0 × 10−7eV·atom−1.Final geometries were minimized using the DMol3 program [40–42] for DFT calculations. Basis set chosen was DNP [43], with GGA/PW91 [44] as exchange functional. Total energy convergence of 1.0 × 10−5 Ha was required, with a 3.7 Å global cutoff. Final cutoff of the SCF cycles was 5.0 × 10−7eV·atom−1, and the orbital cutoff quality was kept equal to 0.1 eV·atom−1. The same starting structure used in GGA/PW91 calculation was employed for hybrid functional B3LYP [45] calculation with 6-311+G(d,p) basis set, now using Gaussian 09. Molden’s processing program [46] was applied, along with Xming emulator [47], to achieve IR continuum spectra.


## 2.2. Development of a Frequency-Weighted Average and Other Useful Tools

A mathematical formula had to be developed in this paper, in order to consider each and every mode belonging to the same 400 cm-1 range, as well as their intensities. Therefore, the use of weighted averages over theoretical data was chosen; its numerical result was calledcentral frequency (cf). With this central frequency, it became possible to consider all theoretical peaks occurring in the vicinity of the diagnostic frequencies, instead of just affirming the existence of the expected band only by naming the most intense theoretical peak. Central frequencies were estimated as follows:
(1)
Central
frequency
=
∑
i
=
1
n
ν
i
×
in
t
i
∑
i
=
1
n
in
t
i
.This mathematical approach (which simply generates a frequency-weighted average) was applied to theoretical frequencies found at ±200 cm−1 around 700, 1000, and 1500 (or 1750) cm−1 and resulted in central frequencies for compounds1–23, which were computed in Table 4 (for GGA/PW91 data) and in Table 5 (for B3LYP data). The mentioned range has been chosen so as to enable each band to complete its 400 cm−1 width, as established in the vibrational theory.


## 3. Results and Discussion

Data will be presented and discussed in three successive sections. In the first section the collection of theoretical IR spectra will be presented. In the second section they will be compared to experimental IR spectra to discuss their precision and accuracy. The third section will deal with the rationalization between musk spectra and musk odor activity. In order to establish such relation, best theoretical IR spectra will be chosen from this paper’s second section.


### 3.1. Part 1: Computation of IR Spectra

Concerningab initio methods, convolved GGA/PW91 spectra are shown in Figure 2, while B3LYP spectra are gathered in Figure 3. For GGA/PW91 spectra, carbon-oxygen single bond stretches occur on frequencies between 1018 cm−1 (for nitro analog21) and 1220 cm−1 (for (4S,7R)-galaxolide7); carbon-nitrogen single bond stretches occur under the frequency of 1200 cm−1 for nitro compounds; carbon-sulfur single bond stretches are observed at 1054 cm−1 for tonkene10. Carbon-carbon double bonds stretches happened at 1687 cm−1 forcis-globanone4 and at 1706 cm−1 fortrans-globanone5, while all other compounds expressing aromatic C=C bonds had their stretching modes between 1543 cm−1 (as in musk ketone11) and 1618 cm−1 (for (4S,7R)-galaxolide7). Nitro groups have presented their symmetric stretching modes near 1310–1340 cm−1 and their nonsymmetric stretching modes at 1520–1560 cm−1. For aldehydes, ketones, ethers, and esters, the carbon-oxygen double bond stretching represents an important mark for confirming spectra: here, the lowest value for such mode is found for tetralin9, at 1680 cm−1, while the highest value, of 1777 cm−1, belongs to acyclic analog20. Carbon-hydrogen bending modes start at very low frequencies and end at 1493 cm−1 (for helvetolide14); simultaneously, the band of carbon-hydrogen stretching modes starts at 2898 cm−1 (for (4S,7R)-galaxolide7) and finishes at 3198 cm−1 (for nitro analog22).Figure 2
Spectra obtained with GGA/PW91 for MCM1–5, PCM6–10, NM11–13, ACM14–16, and nonmusks17–23.Figure 3
Spectra obtained at B3LYP level for MCM1–5, PCM6–10, NM11–13, ACM14–16, and nonmusks17–23.For B3LYP spectra, the lowest frequency found for the carbon-oxygen single bond stretching was 1006 cm−1 (for romandolide15), while its highest frequency was 1403 cm−1 (for tonkene10); the frequency of the carbon-oxygen double bond stretching was found between 1738 cm−1 (for musk8) and 1810 cm−1 (for musk14). The carbon-carbon double bond stretching occurred on the frequency of 1707 and 1718 cm−1 for compounds4 and5 and between 1699 and 1712 cm−1 for compound16; finally, the carbon-carbon double bond stretching for aromatic compounds occurred between 1531 (for non-musk21) and 1650 cm−1 (for musk7). The stretching for nitrogen-oxygen in nitro groups was found at 1250–1417 cm−1 for symmetric modes and at 1531–1618 cm−1 for asymmetric modes. Finally, carbon-hydrogen bending modes began at very low frequencies and went up to 1540 cm−1, at most (for musk13), while carbon-hydrogen stretching occurred between 2953 cm−1 (for compound6) and 3229 cm−1 (for nitromusk13).


### 3.2. Part 2: Comparing GGA/PW91 and B3LYP Spectra to Experimental Data

For an overview over GGA/PW91, B3LYP, and experimental [47] IR data, Figure 4 and Table 2 were built, in which vibrational modes for the most important functional groups are organized in accordance with theoretical method adopted. Each band expresses the range in which labeled vibrational mode occurs, considering the maximum and the minimum found for all compounds. Thus, it becomes possible to state that B3LYP and GGA/PW91 results for C–H stretching modes start at 90 and 140 cm−1, respectively, values that are higher than the ones provided by experimental data; simultaneously, the same band ends at +50 cm−1 for GGA/PW91 and at +90 cm−1 for B3LYP, in comparison to the experimental data. C–H bending modes finish at +30 cm−1 for GGA/PW91 and at +80 cm−1 for B3LYP when compared to experimental values. Aromatic C=C stretches occurred in an expected range for GGA/PW91, with a +20 cm−1 shift for alkene compounds; B3LYP showed a continuous band for alkene and aromatic C=C stretches, which started at +60 cm−1 and ended at +30 cm−1 over experimental data. C–O stretching modes are found within an expected range for both GGA/PW91 and B3LYP methods; for tonkene10, GGA/PW91 predicted C–O mode at 1381 cm−1, while the same mode is found at 1403 cm−1 in B3LYP data. For C=O stretching modes, GGA/PW91 showed a +20 cm−1 increment over lower and higher values found for experimental data, and B3LYP shifted over experimental range in +60 cm−1. Finally, nitro N=O stretching modes have had both symmetric and asymmetric modes accurately and precisely estimated for GGA/PW91; for B3LYP, symmetric nitro stretching showed a broader band than that of GGA/PW91 and of experimental data, starting at a +30 cm−1 shift and finishing at a −10 cm−1 shift, while their asymmetric modes were correctly predicted.Table 2
Collection of observed versus calculated IR mode frequencies for compounds1–23.
Vibrational modea
Observed wavenumber (cm−1) [25]
Calculated wavenumber (cm−1)
GGA/PW91
B3LYP
ν Cb–H
3150–2850
3198–2898
3229–2953
ν C–H (aldehyde)
2900–2800
2954–2892
2988–2939
δ C–H
up to 1465
up to 1493
up to 1540
ν C=C (alkene)
1680–1600
1706–1687
1718–1707
ν C=C (aromatic)
1600–1475
1618–1543
1650–1531
ν C=O (aldehyde)
1740–1720
1715–1693
1772–1749
ν C=O (ketone)
1725–1705
1733–1680
1784–1738
ν C=O (ester)
1750–1730
1777–1742
1810–1768
δ C–O (alcohol, ether, and ester)
1300–1000
1381, 1200–1018
1403, 1312–1006
ν
as nitro (R–NO2)
1660–1500
1560–1520
1618–1531
ν
s nitro (R–NO2)
1390–1260
1340–1310
1417–1250
a
ν: stretching; ν
as: asymmetric stretching; ν
s: symmetric stretching; δ: bending.
b
ν C(sp2)–H, C(sp3)–H, and C(aromatic)–H.Figure 4
Ranges for important vibrational modes collected for compounds1–23 through experimental dataversus GGA/PW91 resultsversus B3LYP results. Vibrational modes come in accordance to bonding atoms and bond order: ingreen, C–H modes; indark green, C=C modes; inlight pink, C–O; inburgundy, C=O; and inblue, N=O modes.Therefore, while GGA/PW91 final results were all fitted into experimental reports, considering the allowed ±30 cm−1 shifts, B3LYP results overestimated C–H stretching and bending modes, alkene C=C stretching modes, and aldehyde and ketone C=O stretching modes.To quantify collected results, experimental IR spectrum given for each particular molecule was compared to its theoretical spectra, as shown in Table3. In the literature—public and personal IR database—only spectra for compounds1–5,8,10, and12 were found. The vibrational modes chosen as internal patterns of comparison were as follows, when occurring: (i) the two most intense peaks regarding the C–O stretching mode; (ii) the most intense peak for the C=O stretching mode; (iii) the most intense peaks for the symmetric and asymmetric C–H stretching modes; (iv) the highest wavenumber found for the C–H bending modes; (v) the highest intensity for the C=C stretching mode; and (vi) the most intense peaks for the symmetric and asymmetric N=O stretching modes. They are altogether able to express theaccuracy relying on theoretical data, once all functional groups have had their modes listed within chosen criteria, and the whole spectrum has been covered.Table 3
Most important wavenumbers for compounds1–5, 8, 10, and 12, according to DFT, B3LYP, and experimental data.
Highest
ν C–0
DIFF
ν C=0
DIFF
ν C–H
DIFF
δ C–H
DIFF
ν C=C
DIFF
ν
s N=O
DIFF
ν
as N=O
DIFF
1
GGA/PW91
1207
1215
28
33
1748
−9
3017
3034
−160
−108
1479
−18
B3LYP
1181
1210
54
38
1786
−47
3033
3069
−176
−143
1517
−56
Exp.
1235
1248
1739
2857
2926
1461
2
GGA/PW91
1099
1231
10
7
1739
−7
2999
3027
−153
−94
1474
−14
B3LYP
1124
1240
−15
−2
1778
−46
3012
3058
−166
−125
1512
−52
Experimental data
1109
1238
1732
2846
2933
1460
3
GGA/PW91
1121
1220
−12
18
1738
−6
2991
3037
−145
−104
1481
−21
B3LYP
1194
1254
−85
−16
1774
−42
3029
3063
−183
−130
1510
−50
Exp.
1109
1238
1732
2846
2933
1460
4
GGA/PW91
1726
−11
2990
3051
−124
−123
1475
−15
1687
B3LYP
1774
−59
3010
3051
−144
−123
1513
−53
1707
Exp.
1715
2866
2928
1460
5
GGA/PW91
1733
−18
2994
3039
−128
−111
1473
−13
1706
B3LYP
1773
−58
3031
3057
−165
−129
1511
−51
1718
Exp.
1715
2866
2928
1460
8
GGA/PW91
1685
5
3005
3083
−115
−122
1483
−13
1594
11
B3LYP
1738
−48
3033
3089
−143
−128
1518
−48
1639
−34
Exp.
1690
2890
2961
1470
1605
10
GGA/PW91
1759
−19
B3LYP
1807
−67
Exp.
1740
12
GGA/PW91
3019
3086
−139
−105
1487
−7
1598
7
1356
4
1547
3
B3LYP
3041
3090
−161
−109
1512
−32
1610
−5
1373
−13
1599
−49
Exp.
2880
2981
1480
1605
1360
1550Table 4
Deviations estimated over differences between experimental and theoretical wavenumbers for GGA/PW91 and B3LYP IR data.
Method
Deviation 1 (cm−1)
Deviation 2 (cm−1)
GGA/PW91
13
124
B3LYP
43
145Table 5
Calculated central frequencies for bands near 700, 1000, and 1500 cm−1 for 1–23 compounds for GGA/PW91 collected data.
Musk
Central frequency (cm−1)
TD*
Around 700
Ave,std.
Diff.
Around 1000
Ave,std.
Diff.
Around 1500
Ave,std.
Diff.
MCM
1
742
743
−1
1030
1049
−19
1429
1411
18
0
2
761
12
18
1096
31
47
1404
11
−7
0
3
748
5
1047
−2
1417
6
0
4
734
−9
1016
−33
1405
−6
0
5
730
−13
1057
8
1402
−9
0
PCM
6
751
733
18
1046
1020
26
1423
1480
−57
0
7
769
34
36
1051
48
31
1424
54
−56
0
8
678
−55
977
−43
1527
47
0
9
731
−2
1066
46
1532
52
0
10
736
3
959
−61
1495
15
0
NM
11
735
755
−20
1033
1019
14
1634
1589
45
0
12
763
17
8
1002
16
−17
1567
39
−22
0
13
766
11
1023
4
1567
−22
0
ACM
14
784
784
0
1084
1086
−2
1402
1411
−9
0
15
762
23
−22
1079
9
−7
1401
16
−10
0
16
807
23
1096
10
1429
18
0
MCa
17
751
743
8
1067
1049
17
1405
1411
−7
0
18
726
12
−17
1049
31
0
1417
11
6
0
Aa
19
779
784
−6
1073
1086
−13
1411
1411
0
0
20
757
23
−28
1105
9
19
1403
16
−8
1
Na
21
733
755
−21
1033
1019
13
1557
1589
−32
0
22
757
17
2
1006
16
−13
1549
39
−40
0
23
717
−38
1060
41
1655
66
2
*TD: total deviations.Extra information comes on the so-called DIFF columns in Table3. Consider
(2)
DIFF
i
=
ExpWavenumber
i
-
TheoWavenumber
i
,
where the difference established between experimental and theoretical values was plotted (for both GGA/PW91 and B3LYP results), as shown in (2). In such equation, for a certain mode i, the difference (DIFF) is obtained through the subtraction of its theoretical value (TheoWavenumber) from its experimental value (ExpWavenumber). The average of the collected differences on Table 3 was estimated as the values of absolute difference were divided by the number of occurring modes, disregarding all C–H stretch modes, as follows:
(3)
Deviation
1
=
∑
i
=
1
n
|
DIFF
i
|
n
.This choice was made due to the fact that all C–H stretches were overestimated in more than 100 cm−1 for both theoretical methods, as discussed before. This last mode, therefore, had its deviation separately estimated as follows:
(4)
Deviation
2
=
∑
i
=
1
n
|
DIFF
i
|
n
in which the absolute DIFF
i is collected, is summed for all C–H stretching modes within the same theoretical method, and is divided by the number of occurring modes.So finally GGA/PW91 IR results are found to be more accurate than B3LYP results, with calculated deviations that are equal to 13 cm−1 and 43 cm−1, respectively. Nevertheless, they correspond to a 3.25% (DFT) and a 10.75% (B3LYP) shift over the 4000–0 cm−1 that represents the spectrum, which ensures that both methods are powerfully predictive. Simultaneously, both methods display great shift over C–H stretching modes, corresponding to an increase of 124 cm−1 and 145 cm−1, respectively. Considering that one of this paper’s aims is to compare theoretical IR data with postulates of the vibrational theory on musky odor, the last mentioned modes are irrelevant, as they are not supposed to be responsible for muskiness.


### 3.3. Part 3: IR Spectra and Musk Activity

Herein, both GGA/PW91 and B3LYP data will be taken into account so as to compare theoretical results with the bands described in the vibrational theory (700, 1000, 1500 or 1750, and 2200 cm−1), which would assign, as supposed by the previous theory, a musky odor to these molecules.In Tables5 and 6 the information was gathered so as to dispose musks1 to23 in lines and their central frequencies (at 700, 1000 and 1500 or 1750 cm−1) in columns. Besides, the compounds were gathered in groups, in accordance with their structural similarity (see first column on the left): MCM for macrocyclic musks, PCM for polycyclic musks, NM for nitromusks, and ACM for acyclic musks. Nonmusks are called MCa for macrocyclic analogs, Aa for acyclic analogs, and Na for nitro analogs. As no vibrational mode has occurred at 2200 ± 200 cm−1, there is no such column.Table 6
Calculated central frequencies for bands near 700, 1000, and 1500 cm−1 for 1–23 compounds for B3LYP collected data.
Musk
Central frequency (cm−1)
TD*
Around 700
Ave,std
Diff.
Around 1000
Ave,std.
Diff.
Around 1500
Ave,std.
Diff.
MCM
1
754
748
6
1142
1093
48
1407
1423
−16
0
2
768
16
20
1066
39
−27
1428
10
5
0
3
749
1
1116
23
1421
−2
0
4
744
−3
1099
5
1430
6
0
5
723
−25
1044
−49
1429
6
0
PCM
6
749
722
28
1068
1019
49
1450
1476
−26
0
7
752
51
31
1052
62
33
1450
32
−27
0
8
692
−30
971
−48
1461
−15
0
9
646
−75
1069
50
1499
23
0
10
768
47
936
−83
1520
44
0
NM
11
754
766
−12
952
977
−26
1602
1597
5
0
12
771
10
5
993
22
16
1595
5
−2
0
13
772
7
987
9
1593
−3
0
ACM
14
722
732
−10
1101
1127
−26
1424
1435
−12
0
15
771
35
39
1130
24
3
1431
14
−4
0
16
703
−29
1149
22
1451
15
0
MCa
17
750
748
2
1067
1093
−26
1418
1423
−5
0
18
726
16
−22
1072
39
−21
1432
10
9
0
Aa
19
784
732
52
1097
1127
−30
1357
1435
−78
1
20
763
35
31
1087
24
−40
1410
14
−26
1
Na
21
742
766
−24
1015
977
38
1601
1597
4
1
22
767
10
1
1150
22
173
1600
5
3
1
23
702
−64
1068
91
1675
78
3
*TD: total deviations.For each musk group, the central frequencies averages (ave, (5)) and their standard deviations (std, (6)) were estimated: these values are plotted at the right side of the central frequency list. The next column on the right shows the differences between each central frequencies and the average of central frequencies (diff, (7)). Consider
(5)
av
e
group
=
1
n
∑
n
=
1
f
c
f
n
,
where c
f
n represents the central frequencies found for each group (MCM, PCM, etc.), having herein been defined lower and upper limits for n, so that n
=
{
1,5
} for MCM; n
=
{
6,10
} for PCM; n
=
{
11,13
} for NM; and n
=
{
14,16
} for ACM. Consider
(6)
st
d
group
=
∑
n
=
1
f
[
(
c
f
n
-
av
e
group
)
2
]
,
(7)
diff
n
=
c
f
n
-
av
e
group
.The values found for theav
e
group and st
d
group of the MCM group were the same as those found for the MCa group; those belonging to NM were repeated for Na; and data calculated for ACM were taken as parameters for Aa.Finally, eachdiff
n value was allowed to be lower or two times its stdgroup value, as stated in
(8)
diff
n
≤
2
×
st
d
group
.If this happens, it is possible to say that theoretical data fit vibrational theory’s demands over study band; if not, they do not agree. When repeating this process for all three bands under the spectra, values for the Total Deviations (TD) are collected. The zero input (0) means that all three bands obeyed (8). Logically, TD inputs between 1 and 3 indicate how many of the bands presented a diff
n value that was higher than the st
d
group doubled value.


### 3.4. Absence of the 2000–2400 cm−1 Band

None of the previous tables bring a mode among the 2000–2400 cm−1 range. The 2200 cm−1 band was described by Turin as the carbonyl stretching mode, which only occurred at this range when working with NDDO/AM1 Hamiltonian. Throughab initio calculation, the mentioned mode was observed at the range of 1680–1810 cm−1, and it was only taken into account for cfs estimates when dealing with the 1550–1950 cm−1 band for nitro compounds. Regarding structural features, compounds6,7,12, and13 do not possess the carbonyl group and are real musks, while compounds17,18,19,20, and23 contain the carbonyl group and are odorless. Therefore, carbonyl stretches cannot be taken as criteria for IR data-musky behavior profile.


### 3.5. GGA/PW91 cf’s Plots and Musk Activity

Table5 (with GGA/PW91 results) presents only two molecules, nonmusks20 and23, which failed to express a complete match between theoretical data and the signed bands of the vibrational theory. For nonmusk20, the cf value estimated near 1000 cm−1 was higher than its avegroup value: this compound had both O–C
sp
2 stretching modes occurring at high intensities and frequencies below 1200 cm−1 (which are precisely the 1090 and 1144 cm−1 wavenumbers). On the other hand, musks14–16 and nonmusk19 have presented a stretch mode (or at least one of them) outside the 1000 ± 200 cm−1 range. Concerning nonmusk23, it can be said that it showed a lower cf value, which remained around the 700 cm−1 band, and a higher cf value, near the 1000 cm−1 band. This can be explained by the fact that, (i) referring to the 700 cm−1 band,23 had an average for intensity modes that was lower than the average values for the other Na and NM compounds, and, therefore, lowerweight values (see (4)) and lower cf; and (ii) referring to the 1000 cm−1 band, the O–C
sp
3 stretch mode at 1073 cm−1 had an intensity value that was 8.7 times higher than the second most intense mode, generating the observed overestimated cf value.That being said and according to mathematical approach adopted in this paper, no relationship was found between IR properties and the presence of musky odor through GGA/PW91. It does not mean that GGA/PW91 calculation leads to affirm that musks and nonmusks have indistinguishable spectra. It means that, considering the weighted-averages values resource in order to simplify the adoption of all theoretical peaks under analysis, resulting central frequencies are similar among musks and nonmusks. Such observation may be due the fact that GGA/PW91 spectra had narrower bands for each vibrational mode rather than B3LYP spectra. As GGA/PW91 proved to be a more accurate method, it requires a more accurate statistical tools, so to properly deal with all theoretical modes, as to affirm (or deny) a possible difference on musks and nonmusks IR spectra.


### 3.6. B3LYP cf’s Plots and Musk Activity

On the other hand, Table6 (with B3LYP data) shows that all musks from1 to16 have had theoretical central frequencies that fitted the frequencies demanded at 700, 1000, and 1500 (or 1750) cm−1 in the vibrational theory. Simultaneously, Aa and Na showed that at least one of their cfs was too shifted from their averages. Molecule23, for instance, is the only nonmusk possessing an aldehyde functional group, and its C=O stretching mode is found at the 1550–1950 cm−1 range under study. Nevertheless, nitro musk11 also holds an aldehyde functional group, and though its cf at 1750 cm−1 is indeed higher than the other cfs for the NM, it is still 70 cm−1 lower than23’s cf. Still concerning the analysis of Table 6, we can say that the acyclic analogs19 and20 have had their central frequencies shifted to lower values at the 1500 cm−1 diagnostic band, the only one in which there was no agreement between theoretical results and expectations deriving from the vibrational theory. At the 1500 ± 200 cm−1 range, hydrocarbon scissoring modes and alkene/aromatic C=C stretching modes are found, and19 and20 lack the gem-methyl at the cyclohexane that are observed in14 and15; moreover, although in16 this gem-methyl is also absent, it possesses two alkene groups, for which its stretching modes are also found at this range. Finally, macrocyclic analogs showed the same spectra data as macrocyclic musks: as compounds18 and19 differ from MCM in that they lack two methylene groups, it is possible to suggest that such loss leads the molecule’s C–H vibrational mode sum to be too low to be detected by its OR, as suggested elsewhere [23]. Besides, both18 and19 present awoody smell; by being smaller, they may be able to bind to a variety of different ORs, which do not reassemble the behavior of the musk, detected by possibly only one OR or just a few more [48].


## 3.1. Part 1: Computation of IR Spectra

Concerningab initio methods, convolved GGA/PW91 spectra are shown in Figure 2, while B3LYP spectra are gathered in Figure 3. For GGA/PW91 spectra, carbon-oxygen single bond stretches occur on frequencies between 1018 cm−1 (for nitro analog21) and 1220 cm−1 (for (4S,7R)-galaxolide7); carbon-nitrogen single bond stretches occur under the frequency of 1200 cm−1 for nitro compounds; carbon-sulfur single bond stretches are observed at 1054 cm−1 for tonkene10. Carbon-carbon double bonds stretches happened at 1687 cm−1 forcis-globanone4 and at 1706 cm−1 fortrans-globanone5, while all other compounds expressing aromatic C=C bonds had their stretching modes between 1543 cm−1 (as in musk ketone11) and 1618 cm−1 (for (4S,7R)-galaxolide7). Nitro groups have presented their symmetric stretching modes near 1310–1340 cm−1 and their nonsymmetric stretching modes at 1520–1560 cm−1. For aldehydes, ketones, ethers, and esters, the carbon-oxygen double bond stretching represents an important mark for confirming spectra: here, the lowest value for such mode is found for tetralin9, at 1680 cm−1, while the highest value, of 1777 cm−1, belongs to acyclic analog20. Carbon-hydrogen bending modes start at very low frequencies and end at 1493 cm−1 (for helvetolide14); simultaneously, the band of carbon-hydrogen stretching modes starts at 2898 cm−1 (for (4S,7R)-galaxolide7) and finishes at 3198 cm−1 (for nitro analog22).Figure 2
Spectra obtained with GGA/PW91 for MCM1–5, PCM6–10, NM11–13, ACM14–16, and nonmusks17–23.Figure 3
Spectra obtained at B3LYP level for MCM1–5, PCM6–10, NM11–13, ACM14–16, and nonmusks17–23.For B3LYP spectra, the lowest frequency found for the carbon-oxygen single bond stretching was 1006 cm−1 (for romandolide15), while its highest frequency was 1403 cm−1 (for tonkene10); the frequency of the carbon-oxygen double bond stretching was found between 1738 cm−1 (for musk8) and 1810 cm−1 (for musk14). The carbon-carbon double bond stretching occurred on the frequency of 1707 and 1718 cm−1 for compounds4 and5 and between 1699 and 1712 cm−1 for compound16; finally, the carbon-carbon double bond stretching for aromatic compounds occurred between 1531 (for non-musk21) and 1650 cm−1 (for musk7). The stretching for nitrogen-oxygen in nitro groups was found at 1250–1417 cm−1 for symmetric modes and at 1531–1618 cm−1 for asymmetric modes. Finally, carbon-hydrogen bending modes began at very low frequencies and went up to 1540 cm−1, at most (for musk13), while carbon-hydrogen stretching occurred between 2953 cm−1 (for compound6) and 3229 cm−1 (for nitromusk13).


## 3.2. Part 2: Comparing GGA/PW91 and B3LYP Spectra to Experimental Data

For an overview over GGA/PW91, B3LYP, and experimental [47] IR data, Figure 4 and Table 2 were built, in which vibrational modes for the most important functional groups are organized in accordance with theoretical method adopted. Each band expresses the range in which labeled vibrational mode occurs, considering the maximum and the minimum found for all compounds. Thus, it becomes possible to state that B3LYP and GGA/PW91 results for C–H stretching modes start at 90 and 140 cm−1, respectively, values that are higher than the ones provided by experimental data; simultaneously, the same band ends at +50 cm−1 for GGA/PW91 and at +90 cm−1 for B3LYP, in comparison to the experimental data. C–H bending modes finish at +30 cm−1 for GGA/PW91 and at +80 cm−1 for B3LYP when compared to experimental values. Aromatic C=C stretches occurred in an expected range for GGA/PW91, with a +20 cm−1 shift for alkene compounds; B3LYP showed a continuous band for alkene and aromatic C=C stretches, which started at +60 cm−1 and ended at +30 cm−1 over experimental data. C–O stretching modes are found within an expected range for both GGA/PW91 and B3LYP methods; for tonkene10, GGA/PW91 predicted C–O mode at 1381 cm−1, while the same mode is found at 1403 cm−1 in B3LYP data. For C=O stretching modes, GGA/PW91 showed a +20 cm−1 increment over lower and higher values found for experimental data, and B3LYP shifted over experimental range in +60 cm−1. Finally, nitro N=O stretching modes have had both symmetric and asymmetric modes accurately and precisely estimated for GGA/PW91; for B3LYP, symmetric nitro stretching showed a broader band than that of GGA/PW91 and of experimental data, starting at a +30 cm−1 shift and finishing at a −10 cm−1 shift, while their asymmetric modes were correctly predicted.Table 2
Collection of observed versus calculated IR mode frequencies for compounds1–23.
Vibrational modea
Observed wavenumber (cm−1) [25]
Calculated wavenumber (cm−1)
GGA/PW91
B3LYP
ν Cb–H
3150–2850
3198–2898
3229–2953
ν C–H (aldehyde)
2900–2800
2954–2892
2988–2939
δ C–H
up to 1465
up to 1493
up to 1540
ν C=C (alkene)
1680–1600
1706–1687
1718–1707
ν C=C (aromatic)
1600–1475
1618–1543
1650–1531
ν C=O (aldehyde)
1740–1720
1715–1693
1772–1749
ν C=O (ketone)
1725–1705
1733–1680
1784–1738
ν C=O (ester)
1750–1730
1777–1742
1810–1768
δ C–O (alcohol, ether, and ester)
1300–1000
1381, 1200–1018
1403, 1312–1006
ν
as nitro (R–NO2)
1660–1500
1560–1520
1618–1531
ν
s nitro (R–NO2)
1390–1260
1340–1310
1417–1250
a
ν: stretching; ν
as: asymmetric stretching; ν
s: symmetric stretching; δ: bending.
b
ν C(sp2)–H, C(sp3)–H, and C(aromatic)–H.Figure 4
Ranges for important vibrational modes collected for compounds1–23 through experimental dataversus GGA/PW91 resultsversus B3LYP results. Vibrational modes come in accordance to bonding atoms and bond order: ingreen, C–H modes; indark green, C=C modes; inlight pink, C–O; inburgundy, C=O; and inblue, N=O modes.Therefore, while GGA/PW91 final results were all fitted into experimental reports, considering the allowed ±30 cm−1 shifts, B3LYP results overestimated C–H stretching and bending modes, alkene C=C stretching modes, and aldehyde and ketone C=O stretching modes.To quantify collected results, experimental IR spectrum given for each particular molecule was compared to its theoretical spectra, as shown in Table3. In the literature—public and personal IR database—only spectra for compounds1–5,8,10, and12 were found. The vibrational modes chosen as internal patterns of comparison were as follows, when occurring: (i) the two most intense peaks regarding the C–O stretching mode; (ii) the most intense peak for the C=O stretching mode; (iii) the most intense peaks for the symmetric and asymmetric C–H stretching modes; (iv) the highest wavenumber found for the C–H bending modes; (v) the highest intensity for the C=C stretching mode; and (vi) the most intense peaks for the symmetric and asymmetric N=O stretching modes. They are altogether able to express theaccuracy relying on theoretical data, once all functional groups have had their modes listed within chosen criteria, and the whole spectrum has been covered.Table 3
Most important wavenumbers for compounds1–5, 8, 10, and 12, according to DFT, B3LYP, and experimental data.
Highest
ν C–0
DIFF
ν C=0
DIFF
ν C–H
DIFF
δ C–H
DIFF
ν C=C
DIFF
ν
s N=O
DIFF
ν
as N=O
DIFF
1
GGA/PW91
1207
1215
28
33
1748
−9
3017
3034
−160
−108
1479
−18
B3LYP
1181
1210
54
38
1786
−47
3033
3069
−176
−143
1517
−56
Exp.
1235
1248
1739
2857
2926
1461
2
GGA/PW91
1099
1231
10
7
1739
−7
2999
3027
−153
−94
1474
−14
B3LYP
1124
1240
−15
−2
1778
−46
3012
3058
−166
−125
1512
−52
Experimental data
1109
1238
1732
2846
2933
1460
3
GGA/PW91
1121
1220
−12
18
1738
−6
2991
3037
−145
−104
1481
−21
B3LYP
1194
1254
−85
−16
1774
−42
3029
3063
−183
−130
1510
−50
Exp.
1109
1238
1732
2846
2933
1460
4
GGA/PW91
1726
−11
2990
3051
−124
−123
1475
−15
1687
B3LYP
1774
−59
3010
3051
−144
−123
1513
−53
1707
Exp.
1715
2866
2928
1460
5
GGA/PW91
1733
−18
2994
3039
−128
−111
1473
−13
1706
B3LYP
1773
−58
3031
3057
−165
−129
1511
−51
1718
Exp.
1715
2866
2928
1460
8
GGA/PW91
1685
5
3005
3083
−115
−122
1483
−13
1594
11
B3LYP
1738
−48
3033
3089
−143
−128
1518
−48
1639
−34
Exp.
1690
2890
2961
1470
1605
10
GGA/PW91
1759
−19
B3LYP
1807
−67
Exp.
1740
12
GGA/PW91
3019
3086
−139
−105
1487
−7
1598
7
1356
4
1547
3
B3LYP
3041
3090
−161
−109
1512
−32
1610
−5
1373
−13
1599
−49
Exp.
2880
2981
1480
1605
1360
1550Table 4
Deviations estimated over differences between experimental and theoretical wavenumbers for GGA/PW91 and B3LYP IR data.
Method
Deviation 1 (cm−1)
Deviation 2 (cm−1)
GGA/PW91
13
124
B3LYP
43
145Table 5
Calculated central frequencies for bands near 700, 1000, and 1500 cm−1 for 1–23 compounds for GGA/PW91 collected data.
Musk
Central frequency (cm−1)
TD*
Around 700
Ave,std.
Diff.
Around 1000
Ave,std.
Diff.
Around 1500
Ave,std.
Diff.
MCM
1
742
743
−1
1030
1049
−19
1429
1411
18
0
2
761
12
18
1096
31
47
1404
11
−7
0
3
748
5
1047
−2
1417
6
0
4
734
−9
1016
−33
1405
−6
0
5
730
−13
1057
8
1402
−9
0
PCM
6
751
733
18
1046
1020
26
1423
1480
−57
0
7
769
34
36
1051
48
31
1424
54
−56
0
8
678
−55
977
−43
1527
47
0
9
731
−2
1066
46
1532
52
0
10
736
3
959
−61
1495
15
0
NM
11
735
755
−20
1033
1019
14
1634
1589
45
0
12
763
17
8
1002
16
−17
1567
39
−22
0
13
766
11
1023
4
1567
−22
0
ACM
14
784
784
0
1084
1086
−2
1402
1411
−9
0
15
762
23
−22
1079
9
−7
1401
16
−10
0
16
807
23
1096
10
1429
18
0
MCa
17
751
743
8
1067
1049
17
1405
1411
−7
0
18
726
12
−17
1049
31
0
1417
11
6
0
Aa
19
779
784
−6
1073
1086
−13
1411
1411
0
0
20
757
23
−28
1105
9
19
1403
16
−8
1
Na
21
733
755
−21
1033
1019
13
1557
1589
−32
0
22
757
17
2
1006
16
−13
1549
39
−40
0
23
717
−38
1060
41
1655
66
2
*TD: total deviations.Extra information comes on the so-called DIFF columns in Table3. Consider
(2)
DIFF
i
=
ExpWavenumber
i
-
TheoWavenumber
i
,
where the difference established between experimental and theoretical values was plotted (for both GGA/PW91 and B3LYP results), as shown in (2). In such equation, for a certain mode i, the difference (DIFF) is obtained through the subtraction of its theoretical value (TheoWavenumber) from its experimental value (ExpWavenumber). The average of the collected differences on Table 3 was estimated as the values of absolute difference were divided by the number of occurring modes, disregarding all C–H stretch modes, as follows:
(3)
Deviation
1
=
∑
i
=
1
n
|
DIFF
i
|
n
.This choice was made due to the fact that all C–H stretches were overestimated in more than 100 cm−1 for both theoretical methods, as discussed before. This last mode, therefore, had its deviation separately estimated as follows:
(4)
Deviation
2
=
∑
i
=
1
n
|
DIFF
i
|
n
in which the absolute DIFF
i is collected, is summed for all C–H stretching modes within the same theoretical method, and is divided by the number of occurring modes.So finally GGA/PW91 IR results are found to be more accurate than B3LYP results, with calculated deviations that are equal to 13 cm−1 and 43 cm−1, respectively. Nevertheless, they correspond to a 3.25% (DFT) and a 10.75% (B3LYP) shift over the 4000–0 cm−1 that represents the spectrum, which ensures that both methods are powerfully predictive. Simultaneously, both methods display great shift over C–H stretching modes, corresponding to an increase of 124 cm−1 and 145 cm−1, respectively. Considering that one of this paper’s aims is to compare theoretical IR data with postulates of the vibrational theory on musky odor, the last mentioned modes are irrelevant, as they are not supposed to be responsible for muskiness.


## 3.3. Part 3: IR Spectra and Musk Activity

Herein, both GGA/PW91 and B3LYP data will be taken into account so as to compare theoretical results with the bands described in the vibrational theory (700, 1000, 1500 or 1750, and 2200 cm−1), which would assign, as supposed by the previous theory, a musky odor to these molecules.In Tables5 and 6 the information was gathered so as to dispose musks1 to23 in lines and their central frequencies (at 700, 1000 and 1500 or 1750 cm−1) in columns. Besides, the compounds were gathered in groups, in accordance with their structural similarity (see first column on the left): MCM for macrocyclic musks, PCM for polycyclic musks, NM for nitromusks, and ACM for acyclic musks. Nonmusks are called MCa for macrocyclic analogs, Aa for acyclic analogs, and Na for nitro analogs. As no vibrational mode has occurred at 2200 ± 200 cm−1, there is no such column.Table 6
Calculated central frequencies for bands near 700, 1000, and 1500 cm−1 for 1–23 compounds for B3LYP collected data.
Musk
Central frequency (cm−1)
TD*
Around 700
Ave,std
Diff.
Around 1000
Ave,std.
Diff.
Around 1500
Ave,std.
Diff.
MCM
1
754
748
6
1142
1093
48
1407
1423
−16
0
2
768
16
20
1066
39
−27
1428
10
5
0
3
749
1
1116
23
1421
−2
0
4
744
−3
1099
5
1430
6
0
5
723
−25
1044
−49
1429
6
0
PCM
6
749
722
28
1068
1019
49
1450
1476
−26
0
7
752
51
31
1052
62
33
1450
32
−27
0
8
692
−30
971
−48
1461
−15
0
9
646
−75
1069
50
1499
23
0
10
768
47
936
−83
1520
44
0
NM
11
754
766
−12
952
977
−26
1602
1597
5
0
12
771
10
5
993
22
16
1595
5
−2
0
13
772
7
987
9
1593
−3
0
ACM
14
722
732
−10
1101
1127
−26
1424
1435
−12
0
15
771
35
39
1130
24
3
1431
14
−4
0
16
703
−29
1149
22
1451
15
0
MCa
17
750
748
2
1067
1093
−26
1418
1423
−5
0
18
726
16
−22
1072
39
−21
1432
10
9
0
Aa
19
784
732
52
1097
1127
−30
1357
1435
−78
1
20
763
35
31
1087
24
−40
1410
14
−26
1
Na
21
742
766
−24
1015
977
38
1601
1597
4
1
22
767
10
1
1150
22
173
1600
5
3
1
23
702
−64
1068
91
1675
78
3
*TD: total deviations.For each musk group, the central frequencies averages (ave, (5)) and their standard deviations (std, (6)) were estimated: these values are plotted at the right side of the central frequency list. The next column on the right shows the differences between each central frequencies and the average of central frequencies (diff, (7)). Consider
(5)
av
e
group
=
1
n
∑
n
=
1
f
c
f
n
,
where c
f
n represents the central frequencies found for each group (MCM, PCM, etc.), having herein been defined lower and upper limits for n, so that n
=
{
1,5
} for MCM; n
=
{
6,10
} for PCM; n
=
{
11,13
} for NM; and n
=
{
14,16
} for ACM. Consider
(6)
st
d
group
=
∑
n
=
1
f
[
(
c
f
n
-
av
e
group
)
2
]
,
(7)
diff
n
=
c
f
n
-
av
e
group
.The values found for theav
e
group and st
d
group of the MCM group were the same as those found for the MCa group; those belonging to NM were repeated for Na; and data calculated for ACM were taken as parameters for Aa.Finally, eachdiff
n value was allowed to be lower or two times its stdgroup value, as stated in
(8)
diff
n
≤
2
×
st
d
group
.If this happens, it is possible to say that theoretical data fit vibrational theory’s demands over study band; if not, they do not agree. When repeating this process for all three bands under the spectra, values for the Total Deviations (TD) are collected. The zero input (0) means that all three bands obeyed (8). Logically, TD inputs between 1 and 3 indicate how many of the bands presented a diff
n value that was higher than the st
d
group doubled value.


## 3.4. Absence of the 2000–2400 cm−1 Band

None of the previous tables bring a mode among the 2000–2400 cm−1 range. The 2200 cm−1 band was described by Turin as the carbonyl stretching mode, which only occurred at this range when working with NDDO/AM1 Hamiltonian. Throughab initio calculation, the mentioned mode was observed at the range of 1680–1810 cm−1, and it was only taken into account for cfs estimates when dealing with the 1550–1950 cm−1 band for nitro compounds. Regarding structural features, compounds6,7,12, and13 do not possess the carbonyl group and are real musks, while compounds17,18,19,20, and23 contain the carbonyl group and are odorless. Therefore, carbonyl stretches cannot be taken as criteria for IR data-musky behavior profile.


## 3.5. GGA/PW91 cf’s Plots and Musk Activity

Table5 (with GGA/PW91 results) presents only two molecules, nonmusks20 and23, which failed to express a complete match between theoretical data and the signed bands of the vibrational theory. For nonmusk20, the cf value estimated near 1000 cm−1 was higher than its avegroup value: this compound had both O–C
sp
2 stretching modes occurring at high intensities and frequencies below 1200 cm−1 (which are precisely the 1090 and 1144 cm−1 wavenumbers). On the other hand, musks14–16 and nonmusk19 have presented a stretch mode (or at least one of them) outside the 1000 ± 200 cm−1 range. Concerning nonmusk23, it can be said that it showed a lower cf value, which remained around the 700 cm−1 band, and a higher cf value, near the 1000 cm−1 band. This can be explained by the fact that, (i) referring to the 700 cm−1 band,23 had an average for intensity modes that was lower than the average values for the other Na and NM compounds, and, therefore, lowerweight values (see (4)) and lower cf; and (ii) referring to the 1000 cm−1 band, the O–C
sp
3 stretch mode at 1073 cm−1 had an intensity value that was 8.7 times higher than the second most intense mode, generating the observed overestimated cf value.That being said and according to mathematical approach adopted in this paper, no relationship was found between IR properties and the presence of musky odor through GGA/PW91. It does not mean that GGA/PW91 calculation leads to affirm that musks and nonmusks have indistinguishable spectra. It means that, considering the weighted-averages values resource in order to simplify the adoption of all theoretical peaks under analysis, resulting central frequencies are similar among musks and nonmusks. Such observation may be due the fact that GGA/PW91 spectra had narrower bands for each vibrational mode rather than B3LYP spectra. As GGA/PW91 proved to be a more accurate method, it requires a more accurate statistical tools, so to properly deal with all theoretical modes, as to affirm (or deny) a possible difference on musks and nonmusks IR spectra.


## 3.6. B3LYP cf’s Plots and Musk Activity

On the other hand, Table6 (with B3LYP data) shows that all musks from1 to16 have had theoretical central frequencies that fitted the frequencies demanded at 700, 1000, and 1500 (or 1750) cm−1 in the vibrational theory. Simultaneously, Aa and Na showed that at least one of their cfs was too shifted from their averages. Molecule23, for instance, is the only nonmusk possessing an aldehyde functional group, and its C=O stretching mode is found at the 1550–1950 cm−1 range under study. Nevertheless, nitro musk11 also holds an aldehyde functional group, and though its cf at 1750 cm−1 is indeed higher than the other cfs for the NM, it is still 70 cm−1 lower than23’s cf. Still concerning the analysis of Table 6, we can say that the acyclic analogs19 and20 have had their central frequencies shifted to lower values at the 1500 cm−1 diagnostic band, the only one in which there was no agreement between theoretical results and expectations deriving from the vibrational theory. At the 1500 ± 200 cm−1 range, hydrocarbon scissoring modes and alkene/aromatic C=C stretching modes are found, and19 and20 lack the gem-methyl at the cyclohexane that are observed in14 and15; moreover, although in16 this gem-methyl is also absent, it possesses two alkene groups, for which its stretching modes are also found at this range. Finally, macrocyclic analogs showed the same spectra data as macrocyclic musks: as compounds18 and19 differ from MCM in that they lack two methylene groups, it is possible to suggest that such loss leads the molecule’s C–H vibrational mode sum to be too low to be detected by its OR, as suggested elsewhere [23]. Besides, both18 and19 present awoody smell; by being smaller, they may be able to bind to a variety of different ORs, which do not reassemble the behavior of the musk, detected by possibly only one OR or just a few more [48].


## 4. Conclusions

This paper worked on developing a method which could state the following: (i) whether musky molecules had their IR theoretical spectra fitted into the four bands assigned by vibrational theory in 2002 Turin’s paper and (ii) whether nonmusky molecules did not have their IR theoretical spectra fitted into same criteria. It was first concluded that only three bands were useful for discriminating musk from nonmusk odorants. The fourth IR band refers to a carbonyl stretching mode, and data here presented showed that this mode cannot be taken as criteria when building a muskiness profile.Present work was carried out with two different functionals applying DFT calculation level, and both were able to accurately predict IR spectra. A mathematical strategy has been adopted in order to summarize IR theoretical data and properly compare musk to nonmusk molecules. Using this approach, GGA/PW91 computed spectra showed no discriminating patterns between musks and nonmusks. B3LYP data showed theoretical frequencies and the three diagnostic bands to be matching, while nitro and macrocyclic nonmusks failed in at least one of such comparisons.It was therefore possible to conclude that no specific mode alone is responsible for the discrimination of the musky odor. Instead, when a great amount of frequencies, expressing weak or medium intensities, were found along the 700–1700 cm−1 range, musk odor occurs. At this range, observed modes were CH2 wag and scissor bending modes, C=C stretches, and symmetric nitro stretching modes.This trial scanning over IR vibrational modes and their relation to musk odor perception brings new informational towards the understanding and application of vibrational theory’s ideas and opens the possibility to a more extensive study, in which a broader number of molecules may be modeled so as to come to a quantitative proposal for a musky-like novel odorant, regarding their IR vibrational modes.



---

*Source: 398948-2014-09-07.xml*