Introduction

The role of radicals in the atmosphere is really important because of their contribution to the creation of environmental problems, e.g., climatic change, air pollution, acid rain, and aerosols [1,2,3].In this regard, the hydroxyl peroxy (HO2) and thioperoxy (HSO, HOS) radicals are among the most important moieties playing a dominant role in the atmospheric pollution [1, 4, 5]. HO2 forms by the interaction of OH radicals with CO in non-polluted areas at low NOx concentrations (>10 ppb) [2, 6].

$$ OH+ CO\to H+C{O}_2 $$
(1)
$$ H+{O}_2\to H{O}_2 $$
(2)

HO2 radicals further interact with O3, which results in the formation of OH radicals. Hydrogen-peroxide generated by the reaction of HO2-radicals is a main source of ozone-depletion and plays an important role in stratospheric and tropospheric oxidation reactions [8,9,10,11,12]. On the other hand, thioperoxy radicals (HOS and HSO) are simple isomeric radicals representative of many sulfur oxo-acids with the composition -[Hx,Sy,Oz], and are of particular interest as potential intermediates in the catalytic depletion of ozone:

$$ HS+{O}_3\to HS O+{O}_2 $$
(3)
$$ HS O+{O}_3\to HS+2{O}_2 $$
(4)

In episulfide oxidations, H2S and the organic-thiols HSO and HOS are intermediates that feed in to the global geobiochemical sulfur cycle and air pollution [4, 5, 13]. There are many reports in the literature on the chemistry of these radicals in the atmosphere [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Hydrogen bonding (HB) is a very significant concept because it can enhance the stability of a radical that migrates far away from its site of generation, and HB can change kinetic behavior by increasing the lifetime of distant molecules [8]. Therefore, literature reports describe many HB-systems, including the combination of SO3, HCl, H2O, NH3, H2SO4 and CH3X (X = halogens) with HO2 radical, and closed or opened-shell HB interactions between HNO and HO2, HCO radicals [16,17,18,19,20,21,22]. The open-shell intermolecular HB of HSO and HO2 radicals was initially reported with formaldehyde and formic-acid, and an SH⋯O blue-shifted HB was identified [23]. Researchers are trying to design various materials for the sequestration of pollutants from the environment, e.g., by loading different organic molecules onto the surfaces of nano materials to tune their sensing properties towards various pollutants, i.e., gases and metals [24,25,26]. Therefore, an understanding of the intermolecular interactions of these organic molecules with various pollutants is really significant for the improved design of such materials.

Carbamic acid (NH2COOH, CA) plays an important role in synthetic and environmental chemistry because of the existence of two protons donors (O–H and N–H) and one acceptor site (C=O) [27]. This molecule is therefor expected to form open-shell HB (OSHB) complexes with HO2, HSO and HOS radicals via three different sites. Analysis of radical–carbamic acid OSHB interactions (HOO⋯CA, HSO⋯CA and HOS⋯CA) may contribute to better interpretation of environmental and synthetic chemistry.

Computational methods

All computations were performed by means of Gaussian-09 software [28]. The geometries of monomers and all complexes were minimized using the opt = verytight option at the unrestricted B3LYP [29], B3PW91 [30] and MP-2 [31] methods by employing standard basis set (6-311++G (d,p)) [32]. A doublet spin state was considered for the OOH, HOS and HSO radicals and their complexes with CA. The nature of all optimized structures was confirmed by performing vibration frequency computations at the B3LYP /6-311++G (d,p) and MP-2/6-311++G (d,p) levels. No imaginary frequency was found for minimized structures, so they are local minima on the corresponding energy surface. Figure 1 represents the structure of an isolated carbamic acid (CA) molecule, indicating sites (S-1, S-2, S-3) where HOO, HOS and HSO radicals are attached for analyzing OSHB. We investigated nine types of complex of CA with HOO, HOS and HSO radical: CA⋯HO2(S-1), CA⋯HO2(S-2), CA⋯HO2(S-3), CA⋯HSO(S-1), CA⋯HSO(S-2), CA⋯HSO(S-3), CA⋯HOS(S-1), CA⋯HOS(S-2) and CA⋯HOS(S-3) (S-1, S-2 and S-3 in parentheses show the attachment of radicals via three different sites of CA). The HB energies (∆Eint) were evaluated by subtracting the total energy of the monomers from the total energy of the complex. All ∆Eint were corrected for basis set superposition error (BSSE) by applying counterpoise (CP) correction [33]. The Truhlar scheme [34] was used for extrapolation of the MP-2/CBS limit by using aug-cc-pVDZ and aug-cc-pVTZ basis sets for both MP2 interaction energies and BSSE. The values used for “alpha” and “beta” were taken from Zhao and Truhlar [35]. The LMOEDA method [36, 37] was used for energy decomposition analysis (EDA) as implemented in the GAMESS US [38, 39] package using the MP2/aug-ccpVDZ method. By performing EDA analysis, the total ∆Eint of each complex was decomposed into electrostatic (ES), repulsion (REP), exchange (EX), dispersion (DISP) and polarization (POL) components.

$$ {\mathrm{E}}_{\mathrm{tot}}=\mathrm{ES}+\mathrm{EX}+\mathrm{REP}+\mathrm{POL}+\mathrm{DISP} $$
(5)
Fig. 1
figure 1

Schematic representation of different sites of carbamic acid (CA). Arrows Sites (S-1, S-2, S-3) where HOO, HOS and HSO radicals are attached

Full size image

Results and discussion

Molecular electrostatic potentials, optimized structures and interaction energies

To obtain insight into the reactivity of a molecule, it is necessary to understand the electrostatic and energetic character of its appropriate known surfaces. Therefore, we computed the electrostatic-potential-maxima and minima (Vs-max and Vs-min) of the CA using the WFA-SAS program [S9]. With the help of the plotted electrostatic potential map shown in Fig. 2, three sites (S-1, S-2 and S-3) were identified for the intermolecular interaction of CA with HO2, HSO and HOS radicals. As seen, there are three electron-deficient and two electron-rich regions on the surface of CA. The molecular electrostatic potential (MEP) values for S-1, S-2 and S-3 are 48.6, 44.5 and 43.6 kcal mol−1, respectively, while the values of Vs-min for S-1 are −38.3 and S-3 is −16.1 kcal mol−1. The MEPs values propose that S-1 is the more-favorable site to interact with the title radicals as compared to S-2 and S-3.

Fig. 2
figure 2

a,b Computed molecular electrostatic potential (MEP) at the 0.001 electrons/Bohr3 contour of CA. a Front view. b Back view. The black sphere on the red region (positive region) shows the most positive region, and the light blue sphere on the dark blue region (negative region) shows the most negative region. Values are in kcal mol−1

Full size image

The optimized structures of monomers and complexes of CA with HOO, HOS and HSO radicals are shown in Fig. 3. All the HB complexes are open-shell systems. The types of HB interaction via the three different sites are XH⋯Y and Y⋯HX (X = O, S and N and Y = O and S). As shown in Fig. 3, all the H-bonded complexes of CA with HOO, HOS and HSO radicals form cyclic structures consist of seven-member rings. The bond lengths are listed in Table 1. The O–H and N–H bond lengths were found to elongate in the complexes, suggesting red-shifted HB. On the other hand, S–H bond lengths decreased upon complex formation, indicating blue-shifted HB in CA⋯HSO complexes at S-1, S-2 and S-3. Note that the amount of O–H bond elongation in HOS complexes is smaller than that in HO2 complexes. The calculated HB distances in the complexes are as follows: in CA⋯OH(S-1): O–H⋯O, O⋯H–O are 1.764, 1.599 Å; in CA⋯HSO(S-1): O–H⋯O, O⋯H–S are 1.756, 2.002; in CA⋯OH(S-2): N–H⋯O, O–H⋯O are 2.031, 1.658 Å; in CA⋯HSO(S-2): N–H⋯O, S–H⋯O are 1.949, 2.044 Å; in CA⋯OH(S-3): O⋯H–O, H–O⋯H are 2.048, 1.796 Å; in CA⋯HSO: O⋯H–N, S–H⋯O are 1.963, 2.313 Å; in CA⋯HOS(S-1): O⋯H–O, O–H⋯S are 1.661, 2.265 Å; in CA⋯HOS(S-2): O–H⋯O, S⋯H–N are 1.697, 2.545 Å; and in CA⋯HOS(S-3): O–H⋯O, S⋯H–N are 1.829, 2.560 Å, respectively. From these HB distances, it is evident that O–H⋯O and O⋯H–O are stronger HBs compared to N–H⋯O, S–H⋯O, O–H⋯S and N–H⋯S HBs. The intermolecular HB angles θ(HB) for all complexes are listed in Table 1. The ideal angle of an HB complex is considered to be 180°. Note that the deviation from 180° is less in O–H⋯O and O⋯H–O H-bond (tilted up to 5–11°) as compared to N–H⋯O and S–H⋯O. The O–H and N–H stretching frequencies (Table S1) imply red shifted HB while the S–H stretching indicate blue shifted HB in the corresponding complexes. A detailed discussion on stretching frequencies analysis is given in the Supporting Information. Interaction energies (∆Eint) were computed using the following equation;

$$ {\Delta \mathrm{E}}_{\mathrm{int}}={\mathrm{E}}_{\mathrm{Complex}}-\left({\mathrm{E}}_{\mathrm{Monomer}\left(\mathrm{A}\right)}+{\mathrm{E}}_{\mathrm{Monomer}\left(\mathrm{B}\right)}\right) $$
(6)

where EComplex is the total complex energy, and EMonomer(A) and EMonomer(B) are the total energies of monomers A and B.

Fig. 3
figure 3

a Optimized geometries of open shell H-bonded (OSHB) complexes obtained at B3LYP/6–311++G** level in S-1, S-2 and S-3. b Key for HBs on S1, S2 and S3 sites

Full size image
Table 1 Optimized geometrical parameters bond lengths (Å) and angles (°) computed at various levels of theories and 6–311++G(d,p) basis set
Full size table

For the H-bonded complexes, ∆Eint were computed with the B-3LYP, B3PW91 and MP-2 method using the 6-311++G (d,p) basis-set. BSSE was applied to correct the ∆Eint values using the CP method [33]. The values of ∆Eint, ∆EintCP and BSSE are given in Table 2. The summarized values reflect that the BSSE values for the B3LYP and B3PW91 methods are consistent with each other, but MP2 results are not as good as they should be: the BSSE values are huge. The BSSE results with the B3PW91 are, of course, expected to be similar to those obtained with B3LYP, as triple-zeta with a couple of polarization functions and diffuse functions is close enough to saturation for DFT-methods. The 6-311++G (d,p) should give as good a DFT as possible, but its performance with MP2 is not better. Apparently, the Pople basis sets (6-31G, 6-311G, etc.) converge to the complete-basis-set limit slower than other schemes. Therefore, to minimize BSSE errors, we employed the MP2/CBS extrapolation scheme of Trauhlar [34] employing aug-cc-pVDZ and aug-cc-pVTZ basis sets. From the MP2/CBS extrapolation, we analyzed the correlations between B3LYP and MP2, which found that the correlation coefficient R has improved from 0.800 to 0.976 (which means that R2 has improved significantly, from 0.638 to 0.953). The correlation results are shown in Fig. 4. The MP2/CBS results for BSSE are collected in Table 2, and are now comparable with those of B3LYP and B3PW91 as presented in Fig. S5.

Table 2 Energetic analysis (kJ mol−1) computed at various levels of theories and basis sets for H-bonded complexes. CBS Complete basis set, BSSE basis set superposition error, EDA energy decomposition analysis
Full size table
Fig. 4
figure 4

Correlation between ΔEint values obtained by the B3LYP/MP2, B3LYP/ MP2(CBS), B3PW91/MP2 and B3PW91/MP2 [complete basis set (CBS)] theories

Full size image

The order of MP2/CBS −∆EintCP kj mol−1 for intermolecular complexes is: CA⋯HO2(S-1) > CA⋯HOS(S-1) > CA⋯HSO(S-1) > CA⋯HOS(S-2) > CA-HO2(S-2) > CA⋯HSO(S-2) > CA⋯HO2(S-3) > CA⋯HOS(S-3) > CA⋯HSO(S-3). Generally, the larger the negative ∆Eint value, the stronger the HB complex. Thus, for all the methods used, the strongest H-bonds are those where the carboxylic acid C=O of CA is an H-acceptor, and H-bonds with S–H and N–H are weaker than those of O–H.

Bader’s AIM analysis

The bond critical points (BCPs), ring critical points (RCPs) and molecular graphs of the OSHB complexes are shown in Fig. 5 (Fig. S2, S3). The values in Table 3 represents topological parameters, such as electron density, Laplacian and the corresponding total energy density values at BCPs. The presence of H-bonds based on the electron density paths and electron density values at the BCP, AIM analysis suggest specific criteria, and that is that ρ and ∇2ρ values are in the range of 0.002–0.035 and 0.024–0.139 a.u., respectively [40, 41]. These are the two basic quantitative criteria that are mostly applied to describe the H-bond strength. The H-bond is considered stronger if the charge density is larger. Table 4 indicates that the electron density (ρ) and Laplacian (∇2ρ) values for the H-bonds of N–H (ρ = 0.0203–0.0298, ∇2ρ = 0.0702–0.1097) and S–H (ρ = 0.0132–0.0251, ∇2ρ = 0.0401–0.0822) are in the suggested range, while for the O–H (0.034–0.0589 and 0.1152–0.1482 a.u.) they exceed the range proposed by Koch and Popelier [40, 41]. This shows that the O–H intermolecular HB is quite stronger.

Fig. 5
figure 5

Molecular graphs and bond paths of OSHB complexes of CA. Green balls Bond critical points (BCP), dark blue balls ring critical points (RCP)

Full size image
Table 3 Quantum theory of atoms in molecules (QTAIM) parameters for HB complexes evaluated at various level of theories and 6–311++G** basis set. Values shown are B3LYP (MP2)
Full size table
Table 4 Stabilization energies (E(2) kcal mol−1) for H-bonded complexes at various level of theories. NBO Natural bond orbital
Full size table

From the analysis of ρ and ∇2ρ values in Table 4, it is clear that, in all three sites of CA, S-1 is more favorable for HB then S-2 and S-3. The strength of HBs is in the order CA⋯HO2(S-1) > CA⋯HO2(S-2) > CA⋯HOS(S-1) > CA⋯HO2(S-2) > CA⋯HSO(S-1) > CA⋯HOS(S-3) > CA⋯HSO(S-2) > CA⋯HSO(S-3). These outcomes are in good agreement with the bond distances, energetic analysis and frequency analysis as discussed above. The correlation of ρ and ∇2ρ with bond lengths is presented in Fig. 6. The correlation plots indicate that there is inverse relationship between bond lengths and ρ and ∇2ρ; when the charge density increases, the overlapping of orbital occurs, due to which the distances decrease. The values for correlation coefficients of ρ and ∇2ρ with hydrogen bond distances are 0.958 and 0.953 for HO2 radical, 0.915 and 0.965 for HSO radical, and 0.909 and 0.969 for HOS radical.

Fig. 6
figure 6

Correlation of electron density (ρ) and its Laplacian (∇2ρ) value with HB distances

Full size image

Total electronic energy density (H) is also very useful to characterize HB [42]. H is a combination of kinetic-energy-density (G) and potential-energy-density (V). We determined the total electronic energy density with the help of a given equation.

$$ \mathrm{H}=\mathrm{G}+\mathrm{V} $$
(7)

Greater negative values of H®) generally indicate stronger H-bond interaction with a partially covalent characteristic, while positive H values shows weak electrostatic interaction involved in the H-bond [42]. The H values listed in the Table 4 are consistent with the geometrical parameters and ∆Eint of the complexes, i.e., the O–H⋯O intermolecular HB is stronger than N–H⋯O and S–H⋯OH-bonds.

Electron density shifts and electron localization function analysis

To explore the characteristics of OSHB interactions, we also computed the electron density shift (EDS) isosurface of the title complexes (Fig. 7). These EDSs were calculated by subtracting the electron densities of the monomers (unperturbed) from the density of the corresponding complex. The blue (positive) and red (negative) regions in the EDS plots correspond to the charge accumulation and depletion, respectively. The plots show that, for the studied complexes, the charge accumulation in between the O and H, S and H regions is large, which reveals the formation of intermolecular H-bonds. Due to the accumulation of charge on the oxygen atom and depletion on the hydrogen atom in O⋯H interactions, the O–H bond is elongated, which is consistent with the bond lengths analysis as discussed above. The EDS results are in good agreement with energetic and AIM analysis, i.e., where C=O acts as an acceptor, and has stronger interactions, and O–H make stronger H-bonds than S–H and N–H.

Fig. 7
figure 7

Electron density difference (EDS) maps of complexes. The blue and red regions represent the increased and depleted electron density, respectively, plotted at isodensity contours 0.0008 electron per Bohr3

Full size image

Figure S4 shows the electron localization function (ELF) for the studied intermolecular HB complexes. It can be seen that the lone pair (LP) electrons of O and S atom are directed towards the H in XH (X = O, S, N) which is consistent with the bond length and AIM analysis.

Noncovalent interaction and reduced density gradient analysis

The 2D reduced density gradient (RDG) plots and 3D noncovalent interaction (NCI) plots of the studied complexes are depicted in Fig. 8. The blue, green and red circles on the 2D and 3D plots represent strong and weak NCIs and steric repulsion in these complexes, respectively. Two spikes are evident from the RDG plot, and the values of spikes are (sign λ2)ρ < 0, which shows a strong interaction. The blue circled spike shows a stronger inter-molecular HB interaction for these complexes as compared to the green circled spike. This justifies the consistency of the results with the AIM and energetic analysis, which show stronger H-bond existence where the O atom act as a H acceptor; O–H group act as H donor values are in the range of −0.04 to −0.05 a.u. Similarly, for the S atom as acceptor and N–H and S–H as H donor the values are in the range of −0.01 to −0.03 a.u., respectively. The RDG and NCI results provide evidence that, on all sites of CA (S-1, S-2 and S-3), O⋯H–O intermolecular H-bonding is the strongest bond as compared to the O⋯H–N, O⋯H–S, S⋯H–O and S⋯H–N H-bonding.

Fig. 8
figure 8

Reduced density gradient (RDG) vs sign (λ2)ρ and noncovalent interaction (NCI) for the complexes: blue, green and red circles shows stronger, weak and repulsive interactions, respectively

Full size image

Natural bond orbital analysis

Natural bond orbital (NBO) analysis is a very convenient tool for the understanding the mechanism of donor-acceptor charge-delocalization, which takes place between the LP of the B and empty antibonding orbital of the σ∗ (A−H) in the H-bonded A–H⋯B system [23]. To investigate the strength of the orbital interaction and the phenomena of red- and blue-shifting and charge transfer in the OH, NH and SH H-bonding, we performed NBO-analysis at MP-2, B-3LYP and B3PW91 methods by employing 6-311++G (d,p) basis set. The values of second-order perturbation energy (E2), are summarized in Table 4.

The E(2) values for O, (LP) → σ* (H–O) charge transfer for S1 in CA⋯HO2 complexes range from 6.79 to 17.44 kcal mol−1 for HB1 and from 4.30 to 13.77 kcal mol−1 for HB2. While in the CA⋯HSO complexes for S1, S2 and S3, the stabilization-energy due to the O (LP) → σ* (H–S) orbital interaction ranges from 3.19 to 9.31 kcal mol−1 for HB1 and from 0.98 to 3.49 kcal mol−1 for HB2. In the CA⋯HOS complexes, the E(2) values for S1, S2 and S3 range from 4.36 to 13.28 kcal mol−1 for HB1 and from 5.54 to 11.56 kcal mol−1 for HB2. The values of E(2) strictly follow the order observed for the interaction energies, i.e., S1 of CA is favorable for H-bond formation with both types of radicals and HO2 radical make the stronger H-bonded complexes then HSO and HOS radicals. These results are consistent with the ρ and ∇2ρ values, which indicate that stronger overlapping of orbitals is related to stronger intermolecular HB.

The NBO analysis results are also in agreement with the results of structural, energetic and AIM analysis, that is, O–H⋯O and O⋯H–O are stronger H-bonds than the others, and S-1 is a more favorable HB site.

Application of EDA

To better understand the nature of the OSHB interactions studied here, the interaction energies were disintegrated into five components, including electrostatic (ES), exchange (EX), repulsion (REP), polarization (POL) and dispersion (DISP). Table 5 summarizes the results of these components. These results prove that, for all the complexes considered, the EX term has the larger values (−17.38 to −41.6 kcal mol−1 for CA⋯HO2 complexes, −15.88 to −31.11 kcal mol−1 for CA⋯HSO complexes and − 17.31 to −33.22 kcal mol−1 for CA⋯HOS complexes, respectively) than other components, which indicates greater overlapping of molecular orbital and suggests stronger orbital interaction in the complexes. After EX, the magnitude of the ES term is larger than those of POL and DISP. The DISP contribution to HB is smaller compared to other components. A comparative plot drawn for the four attractive components (ES, EX, POL and DISP) is represented in Fig. 9. The plot shows the major contribution of EX and ES components in the OSHB complexes. Figure 10 show the correlation plot between EDA and the counterpoise total interaction energy, which are in good agreement (R2 = 0.833). To compare the results of E(2) with the results of EDA indicates that ES and EX terms of EDA increases quickly with E(2) than POL and DISP terms which provide evidences that ES and EX are contributing more for charge transfer.

Table 5 Energy decomposition analysis (EDA; kcal mol−1) for all complexes computed at the MP2/aug-cc-pVDZ level of theory
Full size table
Fig. 9
figure 9

Contribution of various energy components (obtained from EDA) in the OSHB complexes

Full size image
Fig. 10
figure 10

Correlation of MP2(CBS) ΔECP (kcal mol−1) and EDA (kcal mol−1)

Full size image

Conclusions

The OSHB interactions formed between the CA and HO2, HSO or HOS radicals were investigated using MP2, B3PW91 and B3LYP computational methods. It was found that these radicals are attached to three different sites (S-1, S-2, S-3) of CA. Geometry optimization revealed that all the complexes consist of seven-membered rings. From the structural parameters and stretching frequencies analysis, it was observed that OH, NH bonds accompany a red shift, while the SH bond shows a blue shift. OH⋯O H-bonds are comparatively stronger than NH⋯O, SH⋯O, OH⋯S and NH⋯S H-bonds. The counterpoise corrected energies of B3LYP and B3PW91 and MP2/CBS interaction energies showed that H-bonded complexes of site-1(S-1) are more stable. The electron density ρ and corresponding Laplacian ∇2ρ were also computed using the AIM theory, and are in good agreement with structural and energetic analysis that OH⋯O H-bonds are stronger than NH⋯O, SH⋯O, OH⋯S and NH⋯S H-bonds. These results were further supported by NCI/RDG analysis. NBO analysis results coincide with those of structural, energetic and AIM analysis, that OH⋯O is a stronger hydrogen bond than the others, and S-1 is a more favorable site for HB, having higher stabilization energies (E(2))values. EDA analysis indicated that exchange energy makes a larger contribution in the OSHB complexes of CA, which provides the evidence for the larger overlap of orbitals in these systems.