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. 2024 Oct 3;128(41):8865–8877. doi: 10.1021/acs.jpca.4c03615

Photodegradation Pathways of Aliphatic Polyamide through Conical Intersection between Ground and Excited States

Jingcheng Sang †, Yuuichi Orimoto ‡, Yuriko Aoki ‡,*
PMCID: PMC11492239  PMID: 39358900

Abstract

graphic file with name jp4c03615_0010.jpg

Time-dependent density functional theory studies were performed to investigate the photochemistry properties of the widely used aliphatic polyamide (APA), alias nylon, under ultraviolet radiation with N-ethylacetamide (NEA) being the model molecule. The characteristics of the transition molecular orbitals for the low-order excited states (ESs) of NEA were clarified, and the ES geometries related to the transition worthy of study were optimized. Our research proved that there is a conical intersection between the ground and excited states featured by the transition from the lone pair orbital to the σ antibonding orbital on the C–N bond within the peptide group or the N–C bond adjacent to the carbonyl group, and the C–N or N–C bond has the probability to be disrupted after internal conversion. These original quantum chemistry discoveries depict the C–N and N–C bond cleavage scheme that initiates the primary and secondary paths in the scission processes of the APA chain, respectively, which is helpful for giving new insight into the overall photodissociation mechanism of APA and designing advanced polyamide-based synthetic fibers.

1. Introduction

Aliphatic polyamide (APA) owns an indispensable status in the textile, household, and automotive industries, with nylon-66 and nylon-6 being the best known.1−6 Furthermore, APA is also an important component of space equipment, especially in the space suit.7 In most cases, APA has high resistance and durability for abrasion and stretch. However, like many other polymer molecules (rubber, plastic, and so on), APA would be also affected and damaged by photodegradation, thermal degradation, oxidation, and hydrolysis when exposed to the environment for a long time, eventually leading to the destruction of the material microstructure.

Photodegradation experiments on APA have been of interest for many years because APA is vulnerable to ultraviolet (UV) radiation.8−14 Generally speaking, there are three main pathways for the photodegradation mechanism of APA, as summarized in Scheme 1. The hydrogen radical (H·) can be dissociated from the N atom (Path a1) or Cβ atom (Path a2) after the excitation as the initiation of the chain reaction via Path a.1,10,12 In Path a2, the APA radicals would be combined with O2. The APA-O2 radical captures H· from the Cβ atom of any other APA chain (propagation), and the imide will be generated (termination). Furthermore, the H· dissociated from APA would be bound with an other APA molecule to produce the APA-H radical. This process also transfers the radical from one APA molecule to another, but the following degradation reactions are not provided so far.

Scheme 1. Photochemistry Mechanisms of Chain Scission for APA Summarized from the Experiments; Paths a–c Refer to Different Photodegradation Pathways.

Scheme 1

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In Path b, Do et al.10 proposed a new pathway based on experiments on the photodegradation process of APA after the molecule is excited. Chain scission occurs with the N–Cβ bond cleavage, and then the degradation products will be generated. It can be treated as a new initial step for this photodegradation scheme, but the specific photodissociation process for the N–Cβ bond breaking and the following reaction products for Path b has not been discussed further in Do et al.’s research yet. For Path c,8,9,13 the peptide bond in APA would undergo homolytic cleavage to form two radicals (initiation), which would react with each other to form the closed-shell products. In addition, these radicals could be combined with H· from other chains (propagation) to produce the degradation or oxidation products (termination).

Theoretical investigations have been applied to other polymers with the common configuration (carbonyl group), such as polycarbonate.15−17 These studies reported that the C–O single bond in the model molecules is elongated and has the potential to be cleaved in the excited state (ES), which can be treated as the initiation for polymer degradation reactions. Furthermore, our team also found a phenomenon that the electron-withdrawing substituents (for example, −NO2) in the phenyl moiety control the bond length alternation, which can lead to inhibition of the C–O single bond cleavage in the carbonate moiety.17 These results mentioned above implied the feasibility of Path c in the APA photodegradation scheme. However, to the best of our knowledge, all of the initiation mechanisms of the APA chain scission from Paths a–c in Scheme 1 only come from the experiments. Although most of the intermediates of the degradation processes have been depicted by the experiments, the complete photochemistry pathways in Path b for APA are still absent for either the experiment or theoretical study.

Therefore, in order to provide insight into the APA photodegradation, it is worth clarifying the first photoinduced dissociation step in Paths a–c and supplementing the whole degradation mechanisms of APA mainly for Path b with the quantum chemistry (QC) study. This work is principally concentrated on the theoretical analysis of the CC=O–N and N–Cβ bond breakage (initiation) of Paths a and b. Density functional theory (DFT) and time-dependent DFT (TD-DFT) studies were employed to investigate the geometry properties of N-ethylacetamide (NEA), the model molecule of APA (Figure 1b). Transition state (TS) theory and intrinsic reaction coordinate (IRC) analysis were also utilized to specify the final degradation products of the photochemistry pathways shown in Scheme 1. Furthermore, the highlights are the research on the potential energy surface (PES) intersections between the ground state (GS) and ES of APA, which is tightly relevant to the CC=O–N and N–Cβ bond cleavage mechanism of APA under UV radiation in the earth and outer space environment. These theoretical details are elucidated and proposed for the first time.

Figure 1.

Figure 1

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(a) Structural formulas of nylon 66 and nylon 6. (b) Structural formula of NEA used in this QC study. (c) Optimized geometry with the lowest energy for NEA under the GS using the DFT method (calculated at the PBE0/6-31G(d,p) level). The corresponding atom numbers are also denoted.

2. Materials and Methods

2.1. Computational Details

All QC calculations were performed utilizing the Gaussian 16 rev. A.03 software package18 with the restricted (R) and unrestricted (U) DFT/TD-DFT19 method for closed- and open-shell systems, respectively. The PBE0 hybrid functional elucidated by Adamo and Barone20 based on the 1996 pure functional developed by Perdew et al.21 (PBE) was chosen for the QC calculations and is also a popular choice for ES studies.22−24 It should be acknowledged that many DFT methods cannot properly describe the dispersion interactions, and therefore, the dispersion-corrected density functional theory (DFT-D3) proposed by Grimme et al.25 was always applied with the PBE0 functional. The MCSCF scheme was implemented using the state-average complete active space self-consistent field (SA-CASSCF)26 approach to search for the conical intersection (CI)27,28 between the GS and ES with the same spin state, and the SA2-CAS(8,8) calculation details are described in Note S1. The common Pople basis set 6-31G(d,p) was adopted for all the geometry optimizations, TS searches, IRC calculations, PES scans, vibration analyses, and CI verifications. The IRC calculations were carried out to determine whether the reactant, TS, and product could be connected to each other.29 The optimized geometry in the GS (singlet) is denoted as the S0 geometry. The geometry in the nth singlet ES optimized on the basis of the vertical excitations from the GS geometry is denoted as the Sn geometry, and the geometry of the first triplet ES is denoted as T1. To further explore the property of APA in different electronic structures, Mayer bond order30 analysis was also conducted in this work. The UV–vis absorption spectra were plotted using Multiwfn 3.831 and Origin 9.132 software. The structural formula and photodegradation scheme were plotted using ChemDraw in ChemOffice 2021. The molecular geometry illustrations and canonical molecular orbitals (MOs) were rendered utilizing Visual Molecular Dynamics (VMD) 1.9.3 software.33

The Gibbs free energy of each geometry was calculated as follows:

2.1. 1

where the thermodynamic data involving zero-point energy (ZPE), enthalpy variation from 0 K to a certain temperature [H(0 → T)], and entropy (S) for the reactants, TSs, and products at the local minimum and first-order saddle point after the optimization were obtained from the vibration analyses, which were always performed at the fixed calculation level PBE0/6-31G(d,p). The vibration frequencies were retrieved to confirm whether there is only one imaginary frequency for the TS geometry. The frequency scale factors referring to the fitting data for the most approximate level PBE0/6-31G(d) as far as it can be found were introduced to correct the thermodynamic parameters listed above at 298.15 K and 1 atm.34 The calculation method and basis set for the single-point energy of each geometry (εele) were substituted for EOM-CCSD/CCSD35 and def2-TZVP36 to improve the free energy accuracy. Finally, the quasi-RRHO model37 was utilized to perfect the contribution of low frequencies38 to the thermodynamic data in the Shermo 2.4 program.39

2.2. Preparation of the Representative Fragment Molecule

The widely used nylon 66 and nylon 6 with similar molecular configurations were chosen from the aliphatic polyamide family to be the research objects. Because it is tough to treat the polymer as the model compound directly in a QC study, it is necessary to consider how to truncate the APA molecule without impacting its photochemical properties. Because APA is generated by the condensation reaction between the aliphatic amine and the aliphatic acid, the typical characteristic of APA is the repetitive amide separated by the carbon chain. Considering that the CC=O–N bond of APA could be disrupted directly independent of the length of the carbon chain under UV radiation,9,40 the O=C–N–H region is the most important moiety for the properties of APA. The Cα′ and Cβ atoms are also important because the terminal end effects should be suppressed by the CH3 capping. It seems that the Cγ atom is not necessary for the APA photodegradation process shown in Paths a–c in Scheme 1. However, if the Cγ atom is abandoned in this research, it is unfavorable for the study of the subsequent degradation reaction pathways of APA due to the oversimplification of the model molecule. Given the low computation requirements of the truncated model, the Cγ atom is also reserved for this QC calculation. Therefore, the molecule approximation for APA is sufficient for our purpose (yellow dashed box in Figure 1a), although the ES photochemistry could be affected by the difference in the chain length in general, and NEA was chosen as the representative research molecule in this work (Figure 1b). The procedures on how to search and select the NEA geometries at the local minima of the PES are discussed in Note S2, and the NEA geometry with the lowest relative energy is shown in Figure 1c to be the research model in the following QC studies under the GS and ESs.

3. Results and Discussion

3.1. Singlet Vertical Excitation at the GS Geometry

The TD-DFT method was used to obtain the parameters of singlet ESs after the vertical excitation (driven by UV–vis absorption) based on the GS geometry of NEA, and the oscillator strengths (f) of ESs with excitation energy from 5 to 15 eV are shown in Figure 2. Most of the singlet ESs for NEA are in the far UV region (≤200 nm), except for S1. However, APA is known to be damaged experimentally by the radiation from the middle UV region in the vacuum (200–300 nm).41,42 Therefore, the method and basis set dependence for the wavelength deviation of the NEA absorption spectrum were examined, and the discussion is shown in Note S3. It can be concluded that the high-level calculation method has little influence on the wavelength shift of the absorption peak for the NEA molecule in the ES. Therefore, the wavelength deviation of the absorption peak between computation and experiment might be introduced by the huge differences of the molecular size between the polymer APA and small molecule NEA and the molecular environment between APA with the interchain interactions and the isolated NEA molecule.

Figure 2.

Figure 2

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Oscillator strength (f) of each ES with the excitation energy from 5 to 15 eV in the GS geometry. The excitation energy and f of ESs lower than S5 of NEA are marked in this figure in different colors (calculated at the TD-PBE0/6-31G(d,p) level).

It can be seen from the results of the experiment and the TD-DFT study that intense UV radiation (lower than 300 nm) is always essential to excite the NEA molecule. In this QC calculation, only the ESs from S1 to S5 of NEA were chosen as the targets. The vertical excitation energy, f, transition MOs, and their contributions over 2% to these five ESs are listed in Table 1. The f of the S0 → S1 excitation (5.79 eV) is extremely low (0.001) compared with those of other selected ESs. These data indicate that S1 belongs to the dark state and is scarcely possible to excite. In the experiment, nylon 6 or nylon 66 exhibits a weak UV absorption being the first absorption peak with the center at ∼290 nm, and the ES situated in this absorption is associated with the lone pair (n) → antibonding π* orbital transition around the carbonyl group at the same time (Table 1).42 This result demonstrates that the intensity of the UV absorption and the excitation nature of APA in this theoretical study correspond to those in the experiment for S1. Therefore, S1 is not included in the following studies although the S0 → S1 excitation mainly consists of the HOMO → LUMO transition, which should be important in the photochemistry research in general.

Table 1. Parameters of the Vertical Excitations at the GS Geometry Using PBE0/6-31G(d,p) Calculations for NEA.

singlet ES energy (eV) λa (nm) fb contribution (>2%) transition MOc assignmentd
S0 → S1 5.79 214.21 0.001 (0.22) 82.62 H → L n(N&O) → π*(O=C–N)
16.18 H–1 → L
S0 → S2 7.47 165.93 0.150 (2.30) 68.04 H–1 → L n(N&O) → π*(O=C–N)
14.16 H → L
12.75 H → L+1 n(N&O) → σ*(N–H)
S0 → S3 7.78 159.45 0.021 (0.83) 49.88 H–1 → L+1 n(N&O) → σ*(N–H)
38.88 H → L+1
6.82 H–1 → L n(N&O) → π*(O=C–N)
S0 → S4 8.05 153.98 0.045 (1.22) 47.71 H–1 → L+1 n(N&O) → σ*(N–H)
46.96 H → L+1
3.40 H–1 → L n(N&O) → π*(O=C–N)
S0 → S5 9.26 133.90 0.004 (0.33) 83.60 H → L+2 n(N&O) → σ*(C–H)&(N3–C5)
8.01 H–1 → L+2
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a

Wavelength.

b

Transition electric dipole moment components (in Debye) for the three directions X, Y, and Z transformed into the scalar number Inline graphic is given in the parentheses beside f.

c

H and L represent the HOMO and LUMO.

d

Subscripts such as N, O, N–H, and O=C–N represent the MOs populated on these atoms and chemical bonds.

3.2. Leading Excitations for Photodegradation (for Transitions from S0 to S2–S5)

In Figure 3a, the MOs from HOMO–4 to LUMO+3, which cover all the significant transition MOs for the excitations from S0 to S2–S5 in Table 1, are graphically shown with isosurface plots. Regarding the occupied MOs of NEA, the HOMO and HOMO–1 are classified as the same type of orbital [n(N & O)]. For the unoccupied MOs of NEA, the primary compositions of the LUMO, LUMO+1, and LUMO+2 are the antibonding orbitals populated on the C2–N3 bond and O1=C2 double bond [π*(O=C–N)], N3–H4 bond [σ*(N–H)], and N3–C5 and C–H bonds [σ*(N3–C5)&(C–H)].

Figure 3.

Figure 3

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(a) MOs from HOMO–4 to LUMO+3 (isovalue = 0.05) for NEA at the GS (S0) geometry. The major structural parameters of bond length and dihedral angle at these geometries are denoted in this figure, and the main transition MO contribution of the S0 → S2 excitation is also attached (TD-PBE0/6-31G(d,p) level). (b) Excitation, relaxation, and internal conversion pathways for S2 plotted with a Jablonski diagram. The excitation energy and transition nature of S2 (blue), S3 (purple), S4 (brown), and S5 (red) corresponding to those in Figure 2 and Table 1 are tagged beside these ESs. S2ad at 1.52 eV is the adiabatic ES with excitation energy for NEA in S2 after the vertical excitation and relaxation.

The excitation energies and transition natures for ESs from S2 to S5 corresponding to those in Table 1 are plotted in Figure 3b. The S0 → S2 excitation (7.47 eV) is the strongest one among the four ESs, with f ≈ 0.150. Given that the value of f depends on the excitation energy term (Note S4), the transition electric dipole moment components for the transitions from S0 to S1–S5 in the three directions X, Y, and Z based on the GS geometry of NEA are listed in Table S1, and the corresponding scalar numbers Inline graphic are presented in Table 1. These data indicate that the S0 → S2 excitation is probable since it has the strongest transition electric dipole moment.

As the NEA molecule was excited to the Franck–Condon region in S2, this excitation can be assigned mostly as the n(N&O) → π*(O=C–N) transition, with the main contributions from the HOMO–1 and HOMO to LUMO transitions (82.20%), as shown in Table 1. These data imply that the S0 → S2 excitation would mainly contribute to the elongation of the C2–N3 bond and the O1=C2 double bond. Furthermore, the gap between HOMO–1 and LUMO (68.04% contribution of the S0 → S2 excitation; see Figure 3a) is measured as 8.29 (7.06 + 1.23) eV. It is still reasonable that the S2 transition energy of 7.47 eV is a bit smaller than the HOMO–1 → LUMO canonical level difference because the Coulomb interaction between the hole and electron can usually overwhelm the exchange interaction, and thus, the excitation binding energy would lower the energy gap for excitation. After the NEA molecule arrives the local minimum at the PES of S2 (S2ad with 1.52 eV), it is probable for it to be converted from S2 back to S0 by internal conversion (IC in Figure 3b). The characteristics of the transition MOs that account for 88.76% and 94.67% in the S0 → S3 and S0 → S4 excitations (7.78 and 8.05 eV) are all determined by the n(N&O) → σ*(N–H) transition. It suggests that these excitations can facilitate the cleavage of the N3–H4 bond in the ESs of NEA. The S0 → S5 excitation (9.26 eV) is primarily attributed to the HOMO–1 and HOMO → LUMO+2 transitions (91.61%; Table 1). Therefore, the S0 → S5 excitation can be assigned as the n(N&O) → σ*(N3–C5)&(C–H) transition, and thus, it can be speculated that the N3–C5 and C–H bonds could be lengthened in S5.

As mentioned in the Introduction, the photodissociation initial step in Paths a–c has not been extensively investigated and has been rarely discussed by theoretical study. When the side H· removal for the N–H bond in APA is driven by the σ*(N–H) orbital, the S0 → S3 and S0 → S4 excitations must be important to fulfill the photodegradation process in Path a. If the cleavage of the main chain is a leading factor in the APA photodegradation, the corresponding excitations must be strongly related to the S0 → S2 or S5 transition, which leads to the C2–N3 (Path c) or N3–C5 (Path b) bond disruptions by transition nature π*(N–C=O) and σ*(N3–C5), respectively. Hereafter, it is stated that the transition properties and photodissociation mechanisms of Path a (S0 → S3 and S4) will be discussed first, followed by Path b (S0 → S5) and Path c (S0 → S2).

3.3. Side-Group H· Dissociation (S3 and S4 Transitions: Path a)

To obtain the NEA geometry where the bond and dihedral angle would be elongated and rotated in the ES, the NEA geometry shown in Figure 1c was optimized to obtain the conformers at the local minima from S2 to S5 (Figure S4). The major structural parameters of the optimized ES (S3 and S4) geometries are shown in Figure 4a,b. The configuration of the NEA molecule truncated from APA is simple, and the only region worth noting is the peptide bond of NEA. Regarding the critical structural parameters of the S3 and S4 geometries, the N3–H4 bond length (1.77 and 1.73 Å) is extended by 0.76 and 0.72 Å, respectively, compared with the original bond length at the S0 geometry (1.01 Å) (see Figure 3a). The Mayer bond order of the N3–H4 bond is also reduced from 0.884 (S0) to 0.141 (S3) and 0.152 (S4) at the GS and ES geometries, as displayed in Figure 4c. The increasing N3–H4 bond length and decreasing Mayer bond order behaviors in S3 and S4 demonstrate that the H4 atom has an underlying tendency to be dissociated from the N3–H4 bond, eventually leading to the production of two radicals (H· and C4H8NO·) after the N3–H4 bond breakage. In addition, the dominant MOs for the S0 → S3 and S4 transitions and the corresponding ES geometries have interconnected properties, as described in Table 1 and Figure 4b,c. That is, the major structural parameters after the optimizations for S3 and S4 are consistent with the prediction of the N3–H4 bond length elongation based on the transition MOs n(N&O) → σ*(N–H). Although it is not sufficient to claim that the H· will be completely separated from the N3–H4 bond in the S3 and S4 geometries after the PES conversion from the ES to GS, the H· can be combined with a neighboring O atom if the interactions between APA chains are taken into account for experiments.10 Finally, this process also corresponds to the initial photodissociation step of Path a1 in the photodegradation mechanisms of APA in Scheme 1.

Figure 4.

Figure 4

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(a, b) Optimized geometries in (a) S3 and (b) S4 for NEA calculated at the TD-PBE0/6-31G(d,p) level. The key structural parameters (in Å) are tagged beside the figures. (c) N3–H4 Mayer bond orders at the S0, S3, and S4 geometries. (d, e) Relative Gibbs free energy (ΔG) profiles (in kcal/mol) calculated at the CCSD/def2-TZVP level and the possible reaction pathways starting from the combination between the free H· and the C2 atom (d) and the O1 and N3 atom (e) in NEA. The relevant bond lengths and distances between atoms in the reactants, TSs, and products are also shown.

Supposing that the H· could be separated from the N3–H4 bond of NEA in S3 or S4, it is possible for this H· to be combined with another APA chain. When the H· is connected to the C2 atom (Figure 4d), the O1=C2 double bond will be transformed into a single bond and two intermediates (IM1CH and IM1′CH) are generated if the enantiomer is considered during the reactions. Next, the O1=C2 double bond is restored, and the C2–N3 bond is broken after the second reaction. The product with the C2–N3 bond cleavage (denoted by “CH” in this figure) is smoothly produced over two TSs (TS1CH/TS1′CH and TS2CH/TS2′CH) with the reaction barrier always under 17.1 kcal/mol. It is feasible for the reactions to proceed in different enantiomers, although the reaction barrier for the S configuration (11.0 kcal/mol) is a little higher than that for the R configuration (9.5 kcal/mol) for the second reaction in Figure 4d.

In Figure 4e, the O1=C2 double bond is partially disrupted (+0.15 Å) in the intermediate (IM2OH) compared with that of the NEA molecule in the reactants (O + H). Followed by another H transfer reaction from O1 to N3, the O1=C2 double bond is restored and the C2–N3 bond is disrupted. The products with the C2–N3 bond cleavage (“NH”) are also produced over two TSs (TS3OH and TS4OHN) along this reaction pathway. However, compared to the reaction barriers shown in Figure 4e, the reaction barrier from IM2OH to TS4OHN is high (33.3 kcal/mol) for the single-molecule reaction,43 which means that it is hard for the NEA molecule to go through the C2–N3 bond cleavage starting from the bonding between the H· and O1 atoms. If the H· atom reacts with the N3 atom in NEA, the reactant (N + H) could be transformed into the product (NH) with the C2–N3 bond breakage over only one TS (TS5NH). However, it is still a little difficult for the C2–N3 bond cleavage reaction to occur when the H· is combined with the N3 atom due to the higher reaction barrier over TS5NH (22.0 kcal/mol) compared with that for the reaction pathways in Figure 4e. In summary, the APA molecule carrying a H· prefers the triggered chain scission reactions (C2–N3 bond breakage) when the H· is approaching the C2 or N3 atom rather than the O1 atom due to the different reaction barriers.

The first photodissociation step plotted in Path a1 of Scheme 1 has been suggested to be initiated by the S0 → S3 and S4 excitations. It is shown that the N3–H4 bond is adversely influenced and the H· may be dissociated in S3 and S4. Unfortunately, the ES geometry with the significant elongation of the C5–H bond is not observed yet in this study. However, as shown in Figure 3a, the σ*(C–H) component exists in the LUMO+1 (isovalue = 0.05) on the Cβ atom. It can be predicted that the H· could be dissociated from the Cβ atom in Path a2 when APA is excited to an ES higher than S5 irrespective of the high excitation energy.

3.4. Main-Chain CC=O–N and N–Cβ Dissociation (S2 and S5 Transition: Paths c and b)

The variations of the total energy for NEA in S2 with the optimization steps are shown in Figure S4a, and the geometry at the last optimization step for S2 (denoted as “S2(C·N)”) is displayed in Figure S4b. The C2–N3 bond at the S2(C·N) geometry has reached 1.92 Å (+0.56 Å) compared with that at the S0 geometry (Figure 3a). This bond length elongation basically conforms to the initial photodissociation step of Path c in Scheme 1 and the prediction of the C2–N3 bond length elongation for the geometry in S2 based on the nature of the transition MOs [n(N&O) → π*(O=C–N)] in Table 1. Furthermore, a disparate geometry (denoted as “S5(N·C)” in Figure S4c) with the N3–C5 bond cleavage tendency (2.53 Å, +1.08 Å relative to that in S0) is obtained in another optimization for S5 (Figure S4a), which is in line with the initial photodissociation step of Path b in Scheme 1 and the prediction of the N3–C5 bond length variation for the geometry in S5 based on the nature of the transition MOs n(N&O) → σ*(C–H)&(N3–C5). Given the considerable increment of the C2–N3 and N3–C5 bond length variation at the S2(C·N) and S5(N·C) geometries compared with that at the S0 geometry, it is probable for the C2–N3 and N3–C5 bonds of NEA to be cleaved in S2 and S5 followed by the main-chain scission of the APA molecule. Most notably, the S0 → S2 and S0 → S5 excitation energies at the S2(C·N) and S5(N·C) geometries are only 0.025 and 0.003 eV, which implies that there would be a CI between S0 and the singlet ES at the S2(C·N) and S5(N·C) geometries.

To explore the intrinsic properties and the PES crossing behavior of NEA between the GS and different ESs, the PES scan based on the S2(C·N) geometry as a function of the C2–N3 bond length in S0 and S2 is shown in Figure 5d, and the PES scan based on the S5(N·C) geometry with the variation of the N3–C5 bond length in S0 and S5 is shown in Figure 6d. Zoomed-in views of the crucial bond length region are shown in Figures 5a and 6a. The relative energy curve of S2 (blue line) and S5 (red line) sharply drops as the C2–N3 and N3–C5 bonds are elongated to 1.92 and 2.53 Å, while that of S0 based on the same geometry (black line) becomes higher and higher from ∼1.60 Å along the PES scan curve. For the S2(C·N) and S5(N·C) geometries, the total energies of S0 and the singlet ES are almost equal (see the yellow dots in Figures 5a,d and 6a,d) at the same geometry with 0.025 and 0.003 eV excitation energy from S0 to S2 and S5. When the C2–N3 and N3–C5 bonds are elongated over 1.92 and 2.53 Å, the relative energy ordering for the NEA geometry between S0 and the singlet ES will be exchanged, and the relative energy in S0 becomes higher and that of the same geometry in S2 and S5 becomes lower instead. This plot exhibits the circular cone PES landscape between S0 and the singlet ES around the S2(C·N) and S5(N·C) geometries (Figures 5e and 6e), which further demonstrates the existence of a correlated CI.

Figure 5.

Figure 5

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(a) Zoomed-in view of the critical PES scan region in (d) for the potential CI between S0 and S2. (b) Comparison of main Mayer bond orders for NEA based on the S0 geometry, S2(C·N) geometry, and GS geometry with the C2–N3 bond cleavage [S0(C··N)]. The key bond order parameters are denoted in this plot. (c) Zoomed-in view of the crucial PES scan region in (d) for the PES crossing between T1 and S2. (d) Relative energy curves (in kcal/mol) as functions of the C2–N3 bond length (in Å) in S0, T1, and S2 calculated at the (TD-)PBE0/6-31G(d,p) level. The initial geometry utilized in these PES scans was based on the S2(C·N) geometry shown in (e). (e) NEA geometry at the final optimization step for S2 (denoted as the S2(C·N) geometry).

Figure 6.

Figure 6

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(a) Zoomed-in view of the critical PES scan region in (d) for the potential CI between S0 and S5. (b) Comparison of main Mayer bond orders for NEA based on the S0 geometry, S5(N·C) geometry, and GS geometry with the N3–C5 bond cleavage [S0(N··C)]. The key bond order parameters are denoted in this plot. (c) Zoomed-in view of the crucial PES scan region in (d) for the PES crossing between T1 and S5. (d) Relative energy curves (in kcal/mol) as functions of the N3–C5 bond length (in Å) in S0, T1, and S5 calculated at the (TD-)PBE0/6-31G(d,p) level. The initial geometry utilized in these PES scans was based on the S5(N·C) geometry shown in (e). (e) NEA geometry at the final optimization step for S5 (denoted as the S5(N·C) geometry).

To explore the critical point geometry of NEA as the relative energy is near between different electronic states with the same spin multiplicity, the SA2-CAS(8,8)/6-31G(d,p) level calculation was performed to search the CIs correlated to S0 and S2 based on the S2(C·N) geometry and S0 and S5 based on the S5(N·C) geometry. To conform to the transition MO characteristics in the TD-DFT optimizations for S2 and S5, the occupied and unoccupied MO ranking was alternated to optimize the active space in this MCSCF approach, and the results are displayed in Figure S5a,b. The molecular configuration of NEA with the C2–N3 and N3–C5 bond cleavage is basically held compared with the initial S2(C·N) and S5(N·C) geometries. The C2–N3 bond length is further elongated to 2.45 Å at the CI between S0 and S2 (denoted as the “CIS2” geometry), and the C2–N3 bond length is further elongated to 2.72 Å at the CI between S0 and S5 (denoted as the “CIS5” geometry). These data prove that the CIs correlated to S0 and the singlet ESs (S2 and S5) indeed exist, and the NEA molecule can undergo an IC process and then return to the GS at the CI. There are two choices for this relaxation, which are shown in Figures 5a and 6a. First, the total energy is gradually reduced, and NEA can reach the CI toward the GS, which is the same as that in Figure 3a. Second, the C2–N3 or N3–C5 bond length could become longer and longer, eventually leading to the main-chain cleavage.

It is notable that the CI can be sorted as two species of topologies introduced by Ruedenberg et al.44 As can be seen from Figures 5a and 6a, the relative energy curve of S5 would not be significantly declined as the C2–N3 and N3–C5 bond lengths of the S2(C·N) and S5(N·C) geometries are stretched over 1.92 and 2.53 Å. Furthermore, although the C2–N3 and N3–C5 bond lengths of the CI S2 and CIS5 geometries in Figure S5a,b are further elongated over 2.45 and 2.72 Å, the NEA molecule is always relaxed into the GS geometry with C2–N3 or N3–C5 bond recombination using any calculation method. This phenomenon implies that the CI correlated to S0 and the singlet ES (S2 and S5) belongs to the sloped CI45 where the gradients are pointing toward the same direction. Finally, the optimized GS geometries with the C2–N3 bond breaking (denoted by “S0(C··N)”) and N3–C5 bond breakage (denoted by “S0(N··C)”) for NEA were obtained with the procedures shown in Figure S6. The distance between the C2 and N3 atoms at the S0(C··N) geometry is 3.40 Å, and the distance between the N3 and C5 atoms at the S0(N··C) geometry is 4.75 Å; these are much longer compared with those at the S2(C·N) and S5(N·C) geometries (1.92 and 2.53 Å).

Mayer bond orders of several bonds worthy of study in NEA at the S2(C·N), S0(C··N), S5(N·C), S0(N··C), and S0 geometries are shown in Figures 5b and 6b. Since the C2–N3 and N3–C5 bonds have been elongated in the ES relaxation at the S2(C·N) and S5(N·C) geometries, the corresponding Mayer bond orders (0.198 for the C2–N3 bond and 0.087 for the N3–C5 bond) are decreased a lot compared to those of S0 (1.109 for C2–N3 bond and 0.926 for N3–C5 bond), representing a variation of over 80%. On the contrary, the chemical bond between the O1 and N3 atoms lengthens (0.225) at the S2(C·N) geometry, and the C2–N3 bond at the S5(N·C) geometry is strengthened and makes this bond order reach 1.445 instead. These data indicate a tendency for bond cleavage at the S2(C·N) and S5(N·C) geometries, but the orbital interactions still exist between the C2, N3 and C5 atoms. The C2–N3 and N3–C5 bond orders at the S0(C··N) and S0(N··C) geometries are zero, which means that the corresponding C2–N3 and N3–C5 bonds are totally disrupted. These bond order results basically accord with the phenomena mentioned in the last paragraph.

3.5. Intersystem Crossing from S2 and S5 to T1

The crucial PES scan regions for the PES crossings between T1 and the singlet ESs S2 and S5 are magnified in Figures 5c and 6c. The relative energies of the PESs between S2 and T1 (S5 and T1) cross as the C2–N3 (N3–C5) bond of the S5(N·C) (S2(C·N)) geometry is reduced to ∼1.90 (1.85) Å. At this critical geometry, the total energies of S2 and T1 (S5 and T1) are almost the same (see the green dots in Figures 5c and 6c). It is possible for the spin flip of an electron to occur when the NEA molecule is at the energy crossing point (CP) between the singlet and triplet states.46−48 If the spin multiplicity of NEA is switched from 1 to 3, the intersystem crossing (ISC)49,50 will happen between the singlet ES and T1. In this case, the longer the C2–N3 (N3–C5) bond length, the lower the total energy becomes for the triplet NEA geometry at the energy CP. The C2–N3 (N3–C5) bond is completely disrupted in the end.

It is noteworthy that a small total energy peak arises for NEA with the N3–C5 bond length at ∼1.75 Å in T1 and S5 (Figure 6c). This phenomenon suggests that there is the presence of the TS when the N3–C5 bond of the NEA geometry is ∼1.75 Å in T1 and the singlet ES (the excitation energy ordering would be changed from that of S5). Therefore, the NEA geometry around this energy peak (Figure 6c) is regarded as the initial guess to search the TS and calculate the corresponding IRC in T1 and the singlet ES. Finally, the reactant, TS, and product at the IRC leading to the breakage of the N3–C5 bond in T1 and S1 are shown in Figure S7. The N3–C5 bond length of the NEA geometry at the TS in T1 and S1 is ∼2.00 Å, and the N3–C5 bond length is always increased until the bond disruption during the reactions, which is basically consistent with the PES behaviors of T1 and S5 shown in Figure 6c,d. Furthermore, the excitation energy from S0 to S1 of the last NEA geometry at the IRC in S1 (Figure S7a) is 0.022 eV, which indicates that this NEA geometry is close to the CI between S0 and S1. Therefore, the new CI was also calculated with the same SA2-CAS(8,8)/6-31G(d,p) method based on the last NEA geometry at the IRC in S1, and the conformer is displayed in Figure S5. It is evident that the structural parameters of the new CI geometry between S0 and S1 (denoted as “CI”) is different from the old one searched from the S5(N·C) geometry (Figure 5e), which shows that there is more than one CI for NEA with the N–Cβ bond breakage.

The PES overview for the CI correlated to S0 and S2 (S0 and S5) and the energy crossing between T1 and S2 (T1 and S5) of NEA during the PES scan as the C2–N3 (N3–C5) bond is varied for S0, T1, S2, and S5 is plotted in Figure 7a,b. First, the NEA molecule as the model compound of APA is excited vertically from S0 to S2 (S0 to S5) under UV radiation, and it will be relaxed along the orientation of the energy descending at the PES of the ES. There are two possibilities for NEA as it undergoes the energy CP between S2 and T1 (S5 and T1). First, the ISC process can occur, and the spin state of NEA will be changed from singlet to triplet. After further relaxation at the PES of T1, the NEA geometry with C2–N3 (N3–C5) bond cleavage is obtained (Figure 7a,b). Second, when the NEA molecule is relaxed into the S2(C·N) geometry, where the characteristic transition is changed from [n → σ*(O=C–N)] to [n → σ*(C2–N3)] (Table 1 and Figure S8a), it is possible for it to go through the sloped CI within the circular cone PESs between S0 and S2. This photodissociation condition is basically reproduced for the S0 → S2 and S0 → S5 excitations, while the transition nature [n → σ*(N3–C5)] is kept for the S5(N·C) geometry in the S5 relaxation (Table 1 and Figure S8b). Therefore, it is possible for the CC=O–N bond or N–Cβ bond of NEA to be cleaved at the CI after the considerable nonadiabatic coupling pushing the IC process toward the GS. Third, the energy of NEA excited vertically from S0 to S2 or S5 is much higher than the maximum energy along the slope PES of GS if the IC process occurs at the corresponding CI (Figures S4 and S6). The motion of atoms and bond photodissociation would be fast due to the increasing kinetic energy toward the direction of descending gradient. Furthermore, the gradient of the PES in the vicinity of the CI is steep (Figures 5a and 6a), which means that the NEA molecule could pass over this specific CI and stay on the adiabatic PES of S2 or S5. The above-mentioned results indicate that there is another route for the CC=O–N bond or N–Cβ bond of NEA to be disrupted regardless of the CI. After the CC=O–N bond or N–Cβ bond of NEA is further elongated in S2 or S5, it is still possible for the IC process to occur, and the PES of NEA will be converted from the ES to the GS (Figure 7). Finally, the NEA geometry with the C2–N3 (N3–C5) bond cleavage at the probable local minimum of the GS (marked as “S0(C··N)” and “S0(N··C)”) is also displayed in Figures S6a,b and 7a,b.

Figure 7.

Figure 7

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Schematic overviews of the PES profiles for the CIs between the GS and ESs with transition natures [n → σ*(O=C–N)] and [n → σ*(C2–N3)] during the C2–N3 and N3–C5 bond cleavage reactions after the S0 → S2 vertical excitation (a) and photodegradation after the S0 → S5 vertical excitation (b) as the C2–N3 and N3–C5 bond lengths are varied. The red circles near the CIs refer to the circular cone crossing, and the green balls refer to the NEA molecule at different atomic coordinates of the PESs.

3.6. Reaction Pathways Behind N–Cβ Bond Cleavage

As elucidated in sections 3.3 and 3.4, the C2–N3 bond is weakened after the relaxation in S2 (S2(C·N) geometry) and even disrupted after the IC process through the CI toward the GS (S0(C··N) geometry) for NEA. It is noteworthy that the S0(C··N) conformer (Figure S6a) can be associated with the product of the Norrish type I reaction occurring in the ketone51,52 where the CC=O–C bond is disrupted under the UV radiation (Scheme S1a,b). Furthermore, the experiment and ab initio study are consistent that the CC=O–C bond in the ketone will be cleaved in either a singlet or triplet Norrish type I mechanism,53−56 and it is believed that the amide would also undergo the same degradation reaction and produce products parallel to the ketone as the PES of the ketone molecule is switched from the GS to ES at the CI (reaction routes 1–3 in Scheme S1). However, as mentioned in the Introduction, the following degradation products after the photoinduced N–Cβ bond breaking for Path b have been not clarified. Therefore, the reactions following the photodissociation of the N3–C5 bond in S5 for APA were explored to identify the degradation products. The reactants, TSs, and products along the reaction pathways after the vertical excitation of NEA from S0 to S5 are depicted in Figure 8. For the NEA geometry in S5, there are two pathways for the following degradation reactions.

Figure 8.

Figure 8

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Relative Gibbs free energy (ΔG) profiles (calculated at the CCSD and EOM-CCSD/def2-TZVP level in kcal/mol) and the possible reaction pathways after the vertical excitation of NEA from S0 (black) to S5 (red). The important bond lengths and distances between atoms in the reactants, TSs, and products (in Å) are listed, and the reaction barriers for each route are also denoted.

First, if the system does not change the spin state of NEA, the product with the N3–C5 bond cleavage (4.75 Å) in the singlet could be generated (denoted by “S0(N··C)” in this figure) after the IC process at the CI between S0 and S5. Along this H· transfer reaction (black solid line), the H13 atom will be shifted from C7 to C5 over TS1CNC with a 16.8 kcal/mol reaction barrier. The aziridin-2-one and ethane molecules are produced (“CNC”) at the end of the degradation reaction of APA in a singlet (Route (1)).

Second, if the ISC occurs at the energy CP between S5 and T1, then the spin multiplicity of NEA will be switched from 1 to 3. The T1 geometry with N3–C5 bond cleavage (3.18 Å) is obtained (“T1(N··C)”) as the reactant for two degradation reaction routes (gray solid lines). In Route (2), the N3 atom gets close to the C6–H10 bond (TS2CHN), and the H· on the C6 atom is transferred to the N3 atom with a 14.1 kcal/mol reaction barrier. Finally, the acetamide and ethylene in the triplet are produced (3NC). If the spin flip of an electron would happen in ethylene, the most stable product without any radical would be obtained. For Route (3), the C5 atom captures the H· on the N3 atom (TS3NHC), and the H· is moved to the C5 atom with only a 9.5 kcal/mol reaction barrier, which means that this H· transfer reaction is even much easier to occur compared with that in Route (2). The unstable products ethane and acetyl nitrene57 are generated as 3NHC. It is remarkable that the relative energy of the acetyl nitrene in the triplet state is 7.2 kcal/mol lower than that in the closed-shell singlet state (1NHC), which indicates that the triplet acetyl nitrene is more favorable. Therefore, it is still possible for another chain reaction to proceed by grabbing H· from another APA molecule. This phenomenon eventually results in the radical retransfer and the destruction of the polymer structure. It can be seen along these reaction pathways that the C3–N5 bond is completely destroyed in these product systems in either the singlet or triplet electronic state. Finally, the Route (3) process can be defined as the most likely triplet degradation pathway with the reaction barrier at 9.5 kcal/mol.

The APA photodegradation scheme can be assigned into three main pathways (Paths a–c) as investigated and summarized in sections 3.3–3.6, where the H· will be easily dissociated from the N but not the Cβ atom (Path a), and the molecular chain of APA will be directly fractured after the photoinduced N–Cβ bond (Path b) and CC=O–N bond (Path c) disruptions through the CIs between the GS and ESs S5 and S2. Compared with the f of the S0 → S3 and S4 excitations (0.021 and 0.045) in Path a and S0 → S5 excitation (0.004) in Path b, that of the S0 → S2 excitation (0.150) in Path c is much higher, and the S0 → S2 excitation is also favorable in terms of the relatively low vertical excitation energy. Therefore, the possible order of the photodegradation mechanism is Path c (C–N bond breaking by S0 → S2) > Path a (N–H or C–H bond breaking) and Path b (N–C bond breaking by S0 → S5). These results suggest a close link to the experimental conclusion that the C–N bond within the peptide group is the weakest in the polyamide molecule.42

However, as most UV radiation is absorbed by the ozone sphere, the UVB (280–320 nm) and UVC (≤280 nm) make up only 5% and almost 0% of all wavelengths of UV light from outer space reaching earth, and it is tough for APA to be excited in the common working environment. This phenomenon suggests that the thermal and chemical effect (such as hydrolysis) plays a non-negligible role in the APA degradation process.1,10 Therefore, it can be speculated that the photodegradation mechanism for APA would dominate in outer space. In the future, molecular design and modification for APA can be performed to create an energy barrier during any path in the overall photodegradation scheme to prevent the critical S0 → S2 excitation.

Conclusions

The geometry of NEA as the model compound of APA was optimized, and the PES behaviors around the CIs between the GS and ESs were investigated with DFT and TD-DFT studies. The ES geometries differ from each other due to the main transition from the lone pair orbitals n(N&O) to the various antibonding orbitals such as π*(O=C–N) (S1 and S2), σ*(N–H) (S3 and S4), and σ*(N–C) (S5). The ESs from S2 to S5 play the most significant roles in the concise photodegradation scheme, where the correlative chemical bonds in these ESs are elongated, eventually resulting in the photodissociation.

The N–H bond order for NEA in S3 and S4 is severely weakened by the transition MO σ*(N–H). If the H· could be dissociated from the N–H bond and connected to the atoms at the peptide region of another APA chain, then the APA molecule carrying the H· will easily undergo the chain scission reactions. The CI between the GS and ES arises in the S0 → S2 or S5 excitation, and therefore, the nonadiabatic coupling would convert the PES from S2 or S5 to S0 to generate the photodissociation products with the CC=O–N or N–Cβ bond cleavage. Furthermore, there is an energy crossing seam between S2 and T1 (S5 and T1) as the CC=O–N (N–Cβ) bond is elongated from the equilibrium distance, and the APA chain will also be broken after the ISC.

Compared with the secondary path in S5 [n(N&O) → σ*(N–C)], the primary path in S2 [n(N&O) → π*(O=C–N)] should draw more attention due to its strong UV absorption and low reaction barrier in the degradation scheme after the C–N bond disruption within the peptide group of APA. Our theoretical studies as the pioneering work not only excavate the unknown photoinduced degradation mechanisms of APA but are conducive to the application prospect for outer space materials containing APA against UV radiation.

Acknowledgments

This work was funded by the Japan Society for the Promotion of Science (JSPS), the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT) (KAKENHI: JP23245005, JP16KT0059, JP25810103, JP15KT0146, JP16K08321, and JP20H00588), and the Japan Science and Technology Agency (JST), CREST. We thank the Research Institute for Information Technology of Kyushu University on the ITO campus for providing academic HPC resources for this work. The computation was partially performed using Research Center for Computational Science, Okazaki, Japan (Project: 24-IMS-C009).

Glossary

Abbreviations

APA

aliphatic polyamide

CASSCF

complete active space self-consistent field

CI

conical intersection

CP

crossing point

DFT

density functional theory

ES

excited state

GS

ground state

IC

internal conversion

IRC

intrinsic reaction coordinate

ISC

intersystem crossing

MC-SCF

multiconfiguration SCF

MO

molecular orbital

NEA

N-ethylacetamide

PES

potential energy surface

QC

quantum chemistry

TD-DFT

time-dependent DFT

TS

transition state

UV

ultraviolet

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.4c03615.

  • Norrish reaction scheme for ketone; CASSCF orbitals and calculation; optimal NEA conformer search; basis set dependence of electronic absorption spectrum; transition electric dipole moment components in three-dimensional space for the excitation of NEA; variations of excitation energy from S2 to S5 with optimization step; searched CI geometries between GS and ES; fragment radical rotation PES scan based on the S2(C·N) and S5(N·C) geometry; photochemical reaction IRC leading to the N3–C5 bond cleavage searched in S1 and T1; and transition MOs from S0 to S2 and from S0 to S5 based on the S2(C·N) and S5(N·C) geometries, respectively (PDF)

Author Contributions

J.S.: Data curation; formal analysis; original draft writing. Y.O.: Supervision; review & editing. Y.A.: Supervision; review & editing.

The authors declare no competing financial interest.

Supplementary Material

jp4c03615_si_001.pdf (1.1MB, pdf)

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