Introduction

The discoveries of complex molecules in the interstellar clouds have provided valuable new tools for the study of physical conditions in these regions. The molecules are generally believed to be formed on the surfaces of the dust grains in the clouds (Cuppen and herbst 2007; Das and Chakrabarti 2011). The great variety of molecules are found in the densest clouds, particularly in the regions of the galactic center and the Orion nebula. The physical and chemical conditions—including density, temperature, ultraviolet radiation and energetic particles—determine reaction pathways and the complexity of organic molecules in different space environments (Ehrenfreund et al. 2002).

Excluding diatomic molecules, ~30 % of all interstellar molecules have observed isomeric counterparts. These isomers are easily detectable in a number of interstellar environments and readily seen in the spectra of several molecular line surveys.

Molecules with C = C belong to olefins, which are known to be very reactive. Acrylonitrile (2-propenenitrile or vinyl cyanide) is one of the interstellar molecules belonging to olefin group and detected spectroscopically (Jung et al. 2011). It might conceivably undergo reactions like isomerizations to form an isocyanide or a ketenimine, eliminations of HCN or H2, and conversion to HCCCN. Acrylonitrile (CH2CHCN) was first detected in the dense molecular cloud SgrB2 (by Gardner and Winnewisser 1975) and later in TMC1 (Matthews and Sears 1983). Agúndez et al. (2008) observed vinyl cyanide in circumstellar shell of IRC +10216, and Muller et al. (2008) measured the spectra of 13C isotope to identify its presence in Sgr B2(N). The microwave spectrum of vinyl cyanide is discussed in detail by Gardner and Winnewisser (1975). Snyder (2006) also verified the presence of acrylonitrile in the hot molecular core is named the Large Molecule Heimat source, or Sgr B2(N-LMH) by the Interferometric observations (Jobst et al. 2008).

The detection of acrylonitrile or vinyl cyanide (CH2CHCN) shows the possibility of formation of cyanopolynes such as cyanoallene (CH2CCHCN), cyanoacetylene (HCCCN), by the addition of C atom and depletion of H atom respectively, in interstellar space (Singh et al. 2014). Its detection also strengthens the probability of presence of ethylene, the simplest olefin (Gardner and Winnewisser 1975). The formation of cyanopolynes and other carbon chain molecules give the possibility of carbon based chemistry in the universe like earth. However, nitriles can be easily converted to acids by heating in liquid H2O (hydrolysis). Liquid H2O is thought to have been at least briefly present in the asteroidal parent bodies of certain meteorites (Robert and Epstein 1982), and this hydrolysis is a step in various proposed parent body reactions that may lead to amino acids (Ehrenfreund et al. 2001; Bernstein et al. 2004) which are one of the building blocks of proteins - in interstellar dust clouds in our galaxy. The study of prebiotic chemistry for RNA, DNA bases (adenine etc.) and formation of bases, amino acids (such as serine, glycine, alanine etc.) in interstellar medium and molecular clouds has profound implications for understanding the origin of life (Orgel 2004, Chakrabarti and Chakrabarti 2000; Abelson 1966; Glaser et al. 2007). The possibility of formation of above all mentioned molecules give rise to carbon based extraterrestrial life.

The gas phase ion chemistry of acrylonitrile has been studied using several experimental and theoretical methods. The ion-molecule reactions related with acrylonitrile have been investigated by several groups (Jung et al. 2011; Petrie et al. 1992; Hollis et al. 1995; Ervasti et al. 2007, 2009; Gluch et al. 2008; Winnewisser and Gerry 1973; Sun et al. 1993; Jobst et al. 2008). On the surfaces and mantles of dust grains, CH2CHCN, CH3CN, HC2CN and CH3CH2CN are formed as a result of H-addition reactions, thus depleting HC2CN.

Terlouw and co-workers (Ervasti et al. 2007, 2009; Jobst et al. 2008) and Takagi et al. (1999) carried out theoretical studies related to the acrylonitrile radical cation (CH2 = CH–C ≡ N+•). Different experimental techniques like electron attachment (Heni and Illenberger 1986), electron impact ionization (Gluch et al. 2008), charge exchange ionization (Youn et al. (2003), and tandem mass spectrometry (Ervasti et al. 2007, 2009; Jobst et al. 2008; Ichihashi et al. 1995) are used for the characterization of acrylonitrile. A theoretical study of isomerization and dissociation of the acrylonitrile radical cation has also been carried out by Jung et al. (2011) through quantum chemical methods. Petrie et al. (1992) reported the ion molecule reactions of acrylonitrile involving ions relavent to the interstellar cloud chemistry. Youn et al. (2003) have studied the stability of different radicals in interstellar space along with acrylonitrile and found that the radiative life time of acrylonitrile is 970 μsec. The protonated form of the molecule has been argued to exist in high abundances in the upper atmosphere of Titan based on a strong signal at m/z =54 recorded by the ion-neutral-mass spectrometer (INMS) on board the Cassini spacecraft (Vuitton et al. 2006; Vigren et al. 2009).

Simulation of the formation and reactions of molecules and their precursors in the interstellar medium is a difficult task and it is necessary to propose the reactions that can occur at extremely low densities and temperatures. There is a rapidly growing interest for the use of the computational chemistry to study chemical mechanisms and interstellar organic reactions which are difficult to be detected and identified experimentally. It is not an easy task to find thermodynamically feasible step by step reaction mechanisms that can account for formation of acrylonitrile or various other molecules in interstellar medium.

In the present work the quantum chemical calculations are performed to explore the possibility of formation of acrylonitrile in interstellar medium via some detected interstellar molecules such as HCCN and CH2. The free HCCN was first studied by electron spin resonance and UV/IR spectroscopy (Guelin and Cernicharo 1991; Dendramis and Leroi 1977; Merer and Travis 1965). The HCCN is found to be abundant in circumstellar envelop + IRC10216 with coloumn density 1.2 × 1013 cm−2 (Breinhmin et al. 1965). The cyanocarbene (HCCN) is known to exist in high concentration in space and has been identified as the precursor for the formation of the pre-biotic molecules which dictate the reaction pathways for the formation of interstellar prebiotic molecules (Majumdar et al. 2012; Gupta et al. 2011). The CH2 is detected in Orion-KL and W51 M molecular cloud through spectral line detection with column density 1015 and 1014 cm−2 respectively. It is also detected in SgrB2 and W49 N with its low excitation rotational lines in the interstellar medium by far infrared spectroscopy. The column density of CH2 is observed (7.5 ± 1.1) × 1014 cm−2 (Hollis et al. 1995; Polehampton et al. 2005). As such both CH2 and HCCN are well detected and abundant molecules in interstellar medium.

Several studies related to the coupled hydro-chemical model are also present in the literature. These studies explore the possibility of formation of several complex molecules in different regions of the molecular cloud (Das et al. 2008; Majumdar et al. 2013). The grain surface chemistry explored provides insights into the influence that photo dissociation-driven reactions have on the organic chemistry of the interstellar medium. Consider two types of interstellar chemical reactions: 1) grain-surface reactions. 2) gas-phase reactions. In a grain-surface mechanism on cold grains (10 K), simple molecules are formed in ices by single-atom addition reactions because heavier molecules are not mobile. The simple molecules in the ice are photodissociated to form radicals. Upon warming, these radicals become mobile on the ice surface and react via recombination reactions to form larger organic species. Eventually, as the temperature reaches 200–300 K, the ices are evaporated and some gas-phase molecules become ionized (Laas et al. 2011; Garrod et al. 2008; Garrod and Herbst 2006; Hasegawa et al. 1992; Herbst and Leung 1989; Herbst and Klemberer 1973).

Radical-radical reaction mechanism is proposed in this reaction path in gas phase and in icy grains. Using quantum chemical techniques, formation of acrylonitrile has been explored in a single step. In this step of the reaction we have computed the potential energy curve which is barrierless in the present case signifying the possibility of formation of acrylonitrile through this reaction path in interstellar space. The reported reaction path is barrier less and exothermic in both gas phase and ice mentals.

Computational Details

The geometries of the different species involved in the reaction pathway have been obtained at the B3LYP and MP2 level of the theory including all the electrons in the calculations. The B3LYP functional is composed of Becke’s three-parameter hybrid exchange functional (B3) and the correlation functional of Lee, Yang, and Parr (LYP) yields good results in calculations of molecular structure and energetic. In these optimizations 6-311G (d,p) basis set has been employed. Each optimized structure was verified to be a satisfactory point by vibrational analysis carried out at the same level [B3LYP/6-311G (d,p) and MP2/6-311G(d,p)] of theory. Of all hybrid DFT methods, the B3LYP functional is the most widely used (Scott and Radom 1996). MP2/6-311G (d,p) method has been well established over many years because it succeeds in reproducing experimental data with high reliability (Lee et al. 1988; Parr and Yang 1989; Becke 1993). All calculations reported in this work were carried out with the Gaussian03W program package. The chemical analysis calculates the energy requirement for the predicted reaction path; all calculations are performed at room temperature and atmosperic pressure. All the stable geometries were optimized, and confirmed by the vibrational analysis where no imaginary frequency was found. The reaction involved in the present study is exothermic and barrierless and as such do not follow the temperature dependent Arrhenius expression (Bates 1983). The rate coefficient of the proposed reaction is calculated by the Langevin expression which is efficient for the ion-molecule reactions:

$$ \mathbf{K} = \mathbf{7.41}\times \mathbf{1}{\mathbf{0}}^{-\mathbf{1}\mathbf{0}}{\boldsymbol{\upalpha}}^{\mathbf{1}/\mathbf{2}}{\left(\mathbf{10}/\boldsymbol{\upmu} \right)}^{\mathbf{1}/\mathbf{2}}\kern0.75em \mathbf{c}{\mathbf{m}}^{\mathbf{3}}{\mathbf{s}}^{-\mathbf{1}} $$

where α is the polarizability (isotropic polarizability because we are considering the whole molecule having an evenly distributed charge) in A°3 and μ is the reduced mass of the reactants on 12 C amu scale, as suggested by Bates (1983). This expression for the rate coefficient is totally independent of temperature and based on the strong ion-induced dipole long range force. It can be derived by the simple assumption that all collisions leading to capture or orbiting are reactive in nature. The validity of Langevin expression from room temperature and above down to temperatures below 10 K has already been confirmed by experiments (Herbst 2001). Several workers use the “Multiwell program” for calculating the temperature and pressure dependence of reaction rates (Woon and Park 2009; Woon 2006). Their results also indicate that the order of rate constant is not much affected by the temperature variation in the range 10–300 K. There is only a small variation in the magnitude of rate constant. The PCM (Polarization Continuum Model) as implemented in Gassuian03W program has been used to include the bulk salvation effect. Harmonic and anharmonic frequency calculations were also conducted to identify the stable states.

Result and Discussion

The reactions performed in interstellar space are due to the charge transfer process. Observed data is interpreted on the basis of exoergicity rule, which states that an energy resonant or exoergic (∆E ≤0) charge exchange occurs efficiently at low collision energy while endoergic one (∆E ≥0) is hardly observable. In the present work the possibility of formation of acrylonitrile, from HCCN and CH2 radicals, is explored using quantum chemical calculations.

$$ \mathrm{HCCMN}+{\mathrm{CH}}_2\to {\mathrm{CH}}_2\mathrm{CHCN} $$

The optimized geometries of the reactants and product involved in the reaction are schematically shown in Fig. 1 for ground state and excited state respectively and the electronic energies, ZPVE and total energies of all the molecules, radicals at B3LYP/6-311G (d,p) are given in Table 1 for both ground state and excited state.

Fig. 1
figure 1

a Optimized geometries of reactants, product involve in the formation of acrylonitrile in reaction path at B3LYP/6-311G (d,p). b Optimized geometries of reactants, product involve in the destruction of acrylonitrile in reaction path at B3LYP/6-311G (d,p)

Full size image
Table 1 Electronic (EE), Zero Point Vibration (ZPVE) and total energies of molecules and radicals using B3LYP/6-311G (d,p) theory
Full size table

As the quantum chemical calculations show, HCCN reacts with CH2 (carbene like structure) and forms CH2CHCN with a reaction energy of −0.14836 × 102 eV with ZPVE correction in gas phase. ZPE is a much larger piece of energy pie for this molecule. ZPE is also more sensitive to the details of molecular structure than other kinds of corrections so ΔZPE can really affect reaction energies and barriers. Other energy corrections have much smaller effects. Mulliken population analysis of molecule in gas phase show that atomic charge on C (of CH2) atom is −0.149 e.s.u., C (of HCCN) atoms are −0.100 e.s.u., 0.055 e.s.u., and N atom (of HCCN) is −0.226 e.s.u. These atoms can have an electrostatic force of attraction and leads to the formation of CH2CHCN radical in gas phase with energy −46.46548 × 102 eV The calculated dipole moment of the acrylonitrile is 3.9037D which compares well with the experimental value 3.68D reported by Gerry et al. (1979). The rate coefficient of this reaction in gas phase is calculated to be 1.68 × 10−9 cm3s−1.

In PCM also, the HCCN reacts with CH2 and forms CH2CHCN with reaction energy −0.284583 a.u. incorporating ZPVE correction. The electronic energies, ZPVE and total energies of all the molecules, radicals at B3LYP/6-311G (d,p) are given in Table 1. Mulliken population analysis of molecules in PCM or icy grains show that atomic charge on C (of CH2) atom is −0.162 e.s.u., and C (of HCCN) atoms are −0.123 e.s.u., 0.088 e.s.u., and N atom (of HCCN) is −0.311 e.s.u., which are lower than the gas phase. These atoms can have stronger electrostatic force of attraction in comparison to gas phase and leads to the formation of more stable CH2CHCN radical in icy grains with energy −46.46820 × 102 eV The rate coefficient of the reaction in icy grains is calculated to be 1.86 × 10−9cm3s−1 which is higher than the calculated vale in gas phase. This indicates that the higher probability of formation of acrylonitrile with PC model in comparison to the gas phase. The Energy curve of acrylonitrile formation at B3LYP/6-311G (d,p) shown in Fig. 2 in both gas phase and icy phase.

Fig. 2
figure 2

Energy level diagram for reaction path (for gas phase & PCM) at B3LYP/6-311G (d,p)

Full size image

Acrylonitrile formation studied at MP2 level theory gives more accurate results in comparison to the one obtained at B3LYP level. In this theory CH2CHCN forms in gas phase with the reaction energy of −0.08427 × 102 eV with ZPVE correction. The reaction energy calculated at MP2 theory is less than calculated with B3LYP and hence it shows that the high feasibility of acrylonitrile formation under MP2 calculations.

The electronic energies, ZPVE and total energies of all the molecules, radicals for gas phase at MP2/6-311G (d,p) are given in Table 2. Mulliken charge distribution analysis of reactants in gas phase at MP2 theory gives an atomic charge on C (of CH2) atom is −0.179 e.s.u., and C (of HCCN) atoms are 0.039 e.s.u., 0.087 e.s.u., and N atom (of HCCN) is −0.280 e.s.u. As stated earlier, due to electrostatic force of attraction these molecules react and form CH2CHCN radical in gas phase with energy −46.32899 × 102 eV.

Table 2 Electronic (EE), Zero Point Vibration (ZPVE) and total energies of molecules, radicals and transition state using MP2/6-311G (d,p) theory
Full size table
Table 3 Calculated Global and Local reactivity descriptors (eV)
Full size table

With MP2 theory the acrylonitrile forms with the reaction energy −0.303335 a.u. with ZPVE correction. The electronic energies, ZPVE and total energies of all the molecules, radicals for PCM at MP2/6-311G (d,p) level are given in Table 2. The Charge distribution analysis of atoms in molecules involved in the reaction in PCM show an atomic charge on C (of CH2) atom is −0.230 e.s.u., and C (of HCCN) atoms are 0.029 e.s.u., 0.122 e.s.u., and N atom (of HCCN) is −0.341 e.s.u. The negative charge on C5 and positive on C2 generate electrostatic force between both atoms and results the bonding of C5-C2 for acrylonitrile formation with energy −46.33064 × 102 eV in PCM at MP2 level of theory. The energy surface for the formation of acrylonitrile at MP2/6-311G (d,p) level in both gas phase and icy phase is shown in Fig. 3.

Fig. 3
figure 3

Energy level diagram for reaction path (for gas phase & PCM) at MP2/6-311G (d,p)

Full size image

The calculation of global and local reactivity descriptors are performed at B3LYP/6-311G (d,p) and shown in Table 3. The global and local descriptors are very useful and reliable tools for the predication of reaction mechanisms. Thus exploration of global and local reactivity descriptors to understand the mechanistic aspects for the reaction is important. In this context, several reactivity descriptors have been proposed and used to analyse chemical reactivity and site selectivity. Global and local reactivity descriptors evaluated using DFT are very useful in explaining the behavior of reactant and products in an organic reaction. In this regard global electrophilicity, chemical potential, global hardness, global softness, and nucleophilicity are highly successful in predicting the feasibility and polarity of studied reactions

Table 4 Bond lengths and bond angles of all molecular species involved in proposed reaction path by using B3LYP/6-311G (d,p)
Full size table

On the basis of Koopman’s theorem (Parr and Yang 1989) global hardness (η), global softness (S) and global electrophilicity index (ω) are calculated using the energies of frontier molecular orbitals: EHOMO, ELUMO (Parr and Yang 1989; Parr and Pearson 1983; Geerlings et al. 2003; Parr et al. 1999; Chattaraj and Giri 2007). Fukui functions (f k +,f k −,f k 0) local softness (s k +,s k −,s k 0) and local electrophilicity indicies (ω k +,ω k −,ω k 0) have been described earlier in literature (Parr et al. 1999; Chattaraj and Giri 2007). Using Hirshfeld population analyses of neutral, cation and anion state of molecule, Fukui functions are calculated and are shown in Table 3. Fukui function and local electrophilicity/nucleophilicity are extensively applied to probe the local reactivity and site selectivity. Global and local descriptors such as chemical potential, molecular hardness and softness, electrophilicity and condensed Fukui functions have been helpful in predicting the chemical reactivity and regio-selectivity of the HCCN and CH2 radical additions. All the local and global descriptors have been calculated with the well known formulas with the help of “Atoms in Molecule” and “Multiwfn” Softwares. All the formulae are summarized in the paper of Singh et al. 2013

As may be clear from the Table 3 that acrylonitrile is formed with the soft-soft interaction of CH2 and HCCN. The carbon atom (C5) in CH2 has higher philicity than hydrogen atom and the carbon atom (C2) in HCCN contains higher philicity than hydrogen, carbon (C3) and nitrogen atoms. And also C5 atom of CH2 can preferably attack C2 atom of HCCN with Fukui function (f k 0) value 0.6616. As such the most favorable reacting site for acrylonitrile formation will be C2-C5 than any other site.

The proposed reaction path has other possible products which are shown in Fig. 4. But the required product acrylonitrile has the minimum energy among all possible products. The calculated IR spectrum is also shown in Fig. 5 which is agreed well with the observed data (http://www.chemanalytical.com/ft-ir-spectra#Acrylonitrile and also the NTP TR report 2001).

Fig. 4
figure 4

Possible products of the reaction of CH2 and HCOOH at B3LYP and MP2 (Energies in × 102 eV)

Full size image
Fig. 5
figure 5

a FT-IR spectra of Acrylonitrile. b Calculated IR spectra of Acrylonitrile

Full size image

Results obtained with both the level of theories indicate that the acrylonitrile formation under solvent effect is more spontaneous than in gas phase.

All the bond angels and bond lengths (Table 4) of acrylonitrile agree well with observed data of Gerry et al. (1979). Potential energy curve for acrylonitrile has also been shown for its different energy isomers in Fig. 5.

Anharmonic Spectroscopic Constants

The rotational constants of cyanoallene at same level of theory are given in Table 5 & 6. The constants A0, B0 and C0 for the ground vibrational state include the affects of zero-point vibrations and distortions. The rotational constants at the equilibrium geometry of the molecule were calculated at B3LYP/6-311G(d,p) and MP2/6-311G(d,p) levels. Generally due to the anharmonic vibrations the molecule deformed more or less from the equilibrium configuration. The centrifugal force due to the overall rotation acts on component atoms to shift their average positions away from the centre of gravity of the molecule. This force generates some distortions in the molecule and these distortions were calculated by Wilson and developed by Nielsen. The quartic centrifugal distortion constants based on Kivelson-Wilson formalism (Kivelson and Wilson 1952) for acrylonitrile are also given Table 5. The rotation-vibration coupling constants based on the second order perturbative approach (PT2) (Barone 2005) using B3LYP/6-311G (d,p) and MP2/6-311G (d,p) vibrational treatment are given in Table 6. The second order perturbation approximation, the constant α is obtained by taking the difference between the rotational constant in the first excited state of a normal vibration and that in the ground state. The constant α has two uses for molecular structure investigations: it is used for the evaluation of the cubic potential constants and for the determination of the equilibrium structure as already stated.

Table 5 Rotational constants (cm-1) including terms due to quartic centrifugal distortion constant and Nielsen’s-Wilson’s centrifugal distortion constants (×10-6 cm-1 ) of acrylonitrile using B3LYP/6-311G (d,p) and MP2/6-311G (d,p).
Full size table
Table 6 Rotational-vibrational coupling constants (×10-4 cm-1) of acrylonitrile
Full size table

Very small magnitudes of the rotation-vibration constants and Wilson and Nielsen centrifugal distortion constants show that the molecular vibrations of acrylonitrile are almost harmonic in nature.

Vibrational Analysis

A complete vibrational analysis for the molecule has been attempted on the basis of harmonic and anharmonic frequency calculations using the B3LYP/6-311G(d,p) theory. No scaling is needed for the anharmonic frequencies. Vibrational frequencies were scaled by the single scaling factor given by Andersson and Uvdal (2005).

The calculated values have been compared with the experimental frequencies of acrylonitrile Assignments of the vibrational modes have been made on the basis of potential energy distribution (PED) over internal coordinates for the rb3lyp/6-311G(d,p) method. The PED was calculated by using software GAR2PED (Martin and Van Alsenoy 1995). The results are given in Table 7. The following discussion is, therefore, based on B3LYP/6-311G(d,p) calculations.

Table 7 Experimental and calculated infrared spectra of Acrylonitrile. Frequencies in cm-1
Full size table

C-H Vibrations

In the exp IR spectrum of acrylonitrile, CH stretching is observed at 3050 cm−1 which corroborates with the calculated wave number at 3048 cm−1. The rocking mode of CH in experimental band is observed at 1640, 1400 and 1082 cm−1 which corresponds to the calculated vibrational band at 1612, 1390 and 1069 cm−1 respectively. The out of plane wagging mode of CH in experimental data is observed at 681 cm−1 which corroborates to the calculated wave number 689 cm−1.

The scissoring of CH2 observed at experimental band of 1640 and 1400 cm−1 and which corroborates with the calculated vibrational band at 1612 and 1390 cm−1, respectively. The rocking mode of CH2 in experimental band is observed at 1082 cm−1 which corresponds to the calculated vibrational band at 1069 cm−1 respectively.

C-N Vibrations

In the IR spectrum of acrylonitrile, the experimental band for the CN stretching is observed at 2230 cm-1 which corroborates with the calculated band at 2251 cm-1.

Conclusion

Acrylonitrile formation studies at B3LYP and MP2 level of quantum chemical calculations show high probability of its formation through proposed reaction mechanism. The MP2 level theory gives more accurate results in comparison to the one obtained at B3LYP level. The proposed reaction is found to be more feasible in icy grains than in gas phase. The reaction is exothermic and barrierless which increases the probability of feasibility of this reaction in interstellar space. It is also concluded that the proposed reaction, which is feasible and exothermic at room temperature and 1atmosperic pressure, can also have a high probability of the occurrence at the low temperature (<30 K) and pressure (≤1 atm) in interstellar space. In a dense molecular cloud, ices are estimated to receive both particle and photon doses on the order of a few eVmolecule−1 during the cloud’s lifetime. Although the results depend on the conditions of the environment such as radiation field, temperature and pressure, but our study gives qualitative indicators to the formation of acrylonitrile in ISM. Exothermic reaction pathway is most suitable for acrylonitrile formation. Anharmonic spectroscopic parameters such as rotational constants, rotation-vibration coupling constants, and centrifugal distortion constants have been also calculated.

Very small magnitudes of the rotation-vibration coupling constants and Wilson’s and Nielsen’s centrifugal distortion constants show that the molecular vibrations of acrylonitrile are almost harmonic in nature.