Dissociative electron attachment to sulfur dioxide : A theoretical approach
aa r X i v : . [ phy s i c s . a t m - c l u s ] J u l Dissociative electron attachment to sulfur dioxide :A theoretical approach
Irina Jana , Sumit Naskar , Mousumi Das , ∗ andDhananjay Nandi , ∗∗ Department of Physical Sciences, Indian Institute of Science Education andResearch Kolkata, Mohanpur 741246, India. Department of Chemical Sciences, Indian Institute of Science Education andResearch Kolkata, Mohanpur 741246, India.E-mail: ∗ [email protected]; ∗∗ [email protected] Abstract.
In this present investigation, density functional theory (DFT) andnatural bond orbital (NBO) calculations have been performed to understandexperimental observations of dissociative electron attachment (DEA) to SO . Themolecular structure, fundamental vibrational frequencies with their correspondingintensities and molecular electrostatic potential (MEP) map, signifying theelectron density contours, of SO and SO − are interpreted from respective groundstate optimized electronic structures calculated using DFT. The MEPs are thenquantified and the second order perturbation energies for different oxygen lonepair (n) to σ ∗ and π ∗ interactions of S-O bond orbitals have been calculatedby carrying out NBO analysis and the results are investigated. The change inthe electronic structure of the molecule after the attachment of a low-energy ( ≤
15 eV) electron, thus forming a transient negative ion (TNI), can be interpretedfrom the n → σ ∗ and n → π ∗ interactions. The results of the calculations areused to interpret the dissociative electron attachment process. The dissociationof the anion SO − into negative and neutral fragments has been explained byinterpreting the infrared (IR) spectrum and the different vibration modes. Itcould be observed that the dissociation of the anion SO − into S − occurs as aresult of simultaneous symmetric stretching and bending modes of the molecularanion. While the formation of O − and SO − occurs as a result of anti-symmetricstretching of the molecular anion. The calculated symmetries of the TNI statecontributing to the first resonant peak at around 5.2 eV and second resonantpeak at around 7.5 eV could be observed from time-dependent density functionaltheory (TD-DFT) calculations to be an A and a combination of A +B states forthe two resonant peaks, respectively. These findings strongly support our recentexperimental observations for DEA to SO using the sophisticated velocity mapimaging (VMI) technique [Jana and Nandi, Phys. Rev. A, 2018, , 042706 ]. issociative electron attachment to sulfur dioxide : A theoretical approach
1. Introduction
Sulfur dioxide is a bent molecule with O-S-O bond an-gle of 119.3 and S-O bond length of 143.1pm hav-ing a C v symmetry with ground state configuration(7a ) ,(1a ) ,(4b ) ,(8a ) [1]. The presence of sul-fur dioxide in starting from acid rain to natural vol-canic sources, makes it one of the most important at-mospheric molecules [2]. Recording the vibrationalbands and molecular constants of SO from the in-frared (IR) spectrum of the molecule using an infraredprism-grating spectrometer have been reported sincethe early 1950’s [3]. Robert et al. also reported IR thespectrum of anhydrous liquid sulfur dioxide and anhy-drous liquid hydrogen fluoride using a Perkin-Elmer,Model 21, double beam recording infrared spectrome-ter [4]. Recently, in the year 2014, Zhu et al. reporteddensity functional theory (DFT) and natural bond or-bital (NBO) calculations to study the electronic struc-tures and bonding interactions between sulfur dioxidemolecule and ruthenium (II) atom in two ruthenium-SO adducts [5]. Using the molecular structure, vibra-tional spectra and molecular electrostatic potential tostudy large polyatomic molecules like metolazone us-ing the Gaussian 03 program package can be observedin the literature [6]. Ab initio calculations to investi-gate the enhancement of halogen bonds by σ -hole and π -hole interactions between two molecules containinghalogen atom in one, and a negative site in another hasbeen reported by Esrafili and Vakili where, molecularelectrostatic potential (MEP) of isolated SO has beencomputed [7].Study of low-energy ( ≤
15 eV) electron attach-ment to SO has been a topic of interest since the early1970’s. There have been many experimental studiesreporting dissociative electron attachment (DEA) toSO [1, 8–13]. Experiments on DEA to SO is knownto produce two prominent resonant peaks at around5.2 and 7.5 eV as explained by the following reaction: SO + e − −→ SO −∗ −→ S − + O O − + SOSO − + O (1)where a low-energy electron gets attached to the SO molecule via a resonant capture forming SO −∗ . Thiscomplex SO −∗ , called the transient negative ion (TNI),then dissociates giving neutral and anionic fragments.Experiments reporting electron attachment cross-section of the negative ion fragments produced fromDEA to SO and also the corresponding kinetic en-ergies of the fragments using different processes areabundant in the literature [8–12]. Although experi-ments reporting angular distribution of the fragments are scarce [14]. But theories reporting DEA to SO are very less in the literature [1, 15]. In the year 1996,Krishnakumar et al. using ab initio molecular orbitalcalculations and selection rules for dissociative electronattachment reported the first resonance between 4-5 eVto be due to A and the second peak at around 7 eVto be due to B negative ion resonant states [1]. Re-cently, Jana and Nandi reported DEA to SO using thesophisticated velocity map imaging (VMI) and identi-fied the first resonance around 5.2 eV due to an A andthe second resonance around 7.5 eV due to a combina-tion of A + B negative ion resonant states [13].We report a theoretical and computationalapproach to find out the optimized ground statemolecular structure of neutral SO molecule and itsanionic part SO − formed after the attachment of alow energy electron to the molecule using Gaussian 09program package [16]. The density functional theory(DFT) calculation has been performed using the Becke3LYP exchange-correlational functional containing theSlater exchange functional, Hartree-Fock and Becke’s1988 gradient correction, along with the Lee-Yang-Parr functional with a aug-cc-pVQZ basis set toobtain a stable structure [17–22]. The results ofthese calculations are then used to find out change inthe ground state electronic structure of the moleculeafter the electron attachment. The electron densitydistribution is then visualized for the neutral SO molecule and the SO − TNI with the help of themolecular electrostatic potential (MEP) map. Theelectron density distribution has been quantified withthe help of natural bond orbital (NBO) analysis,followed by bond order calculation and Mulliken chargeanalysis. A vibration spectral analysis is then carriedout using the computed infrared (IR) spectrum, toinvestigate different vibration modes of the TNI andhence identify the formation of different negative andneutral fragments given by Eqn. 1. The potentialcurves for the first two dissociation pathways ofEqn. 1 have also been plotted for the neutral parentmolecule and the optimized ground state configurationof the TNI, by varying the O-O and S-O bonddistances, respectively. Finally, a time-dependentdensity functional theory (TD-DFT) calculation hasbeen performed to calculate the vertical excited stateenergies of SO − TNI and thus identify the negative ionresonant states of the TNI involved in DEA to SO atthe first and second resonant peaks.
2. Modeling of the molecule and densityfunctional theory
Density functional theory (DFT) calculations to smallpolyatomic molecules is abundant in the literature. In issociative electron attachment to sulfur dioxide : A theoretical approach ab initio electronic structure calcula-tion using DFT has been performed to neutral SO andits anionic part SO − using Gaussian 09 program pack-age [16]. Quantum chemical calculations using DFT isan efficient tool in illuminating not only the electronicstructure of the SO molecule, but also how the neu-tral molecule reacts to the incoming low-energy elec-tron thus forming the TNI state. It is well known thatthe electronic structure of anions can be obtained usingDFT [23]. First, the ground state geometries of SO and SO − molecules were optimized using DFT withthe Becke 3LYP exchange-correlational functional witha aug-cc-pVQZ basis set to obtain a stable structure.The ground state optimized energy for SO comes outto be -548.733 Hartree while the optimized energy forground state of SO − comes out to be -548.785 Hartree.Thus the optimized ground state energy of SO − is 1.42eV lower than the ground state optimized energy ofthe neutral molecule. This indicates that the adiabaticelectron affinity of SO is positive and given by the dif-ference value of 1.42 eV. This matches excellently withGrabowski et al. who measured the electron affinityof SO to be 1.1 ± molecule.Considering the Lewis structure of SO molecule(Fig. 1) it can be observed that the bent structure ofthe molecule is such that the S-atom has a less electro-negativity while the bottom O-atoms have more of it.This makes the SO molecule polar. This charge differ-ence and the distance between the charge centers pro-duces a large permanent dipole moment. The dipolemoment of SO is computed to be 1.7473 D while thetheoretical dipole moment reported by McConkey etal. is 1.63305 D [2]. Thus the dipole moment of theneutral molecule matches satisfactorily with the earlierreported value. As a low-energy electron gets attachedto the SO molecule forming a TNI, the charge distri-bution of the molecule as a whole changes and so doesthe dipole moment. The dipole moment of the opti-mized SO − ground state is observed to be 1.4481 D.This 0.30 D decrease can be attributed to the attach-ment of the negative charge.The present calculation recognizes the SO groundstate to be an A state while the SO − as a B state.This identification is in well-agreement with Guptaand Baluja [15]. The highest occupied molecularorbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for these configurations are 8a and9b respectively, for both SO and SO − molecules,as shown in Fig. 2. The gap between the HOMOand LUMO for SO ground state optimized geometryis 5.12 eV while, for SO − ground state optimizedgeometry it is 2.78 eV. The HOMO of SO − rises byan amount of 9.97 eV and the LUMO of SO − rises byan amount of 7.63 eV as compared to the respectiveHOMO and LUMO values of SO , making the TNISO − more stable.Figure 2: (a) 3D visualization of the HOMO and(b) 3D visualization of the LUMO orbitals of SO − molecule. The yellow sphere represents the S-atom andthe red spheres represent the O-atoms.The calculated geometries of the SO molecule andSO − negative ion are shown in Fig. 3(a) and Fig. 3(b),respectively. The neutral SO molecule has C v sym-metry with a S-O bond length of 1.44 ˚ A and 118.68 O-S-O bond angle in the optimized state (Fig. 3(a)).After the attachment of the electron, the anion retainsthe C v symmetry but the S-O bond length increasesby 0.08 ˚ A while the O-S-O bond angle decreases by4.7 (Fig. 3(b)) [13]. While the direction of the dipolemoment remains same in both the cases and is repre-sented by the red arrow in Fig. 3(a) and Fig. 3(b).
3. Molecular electrostatic potential
The change in the dipole moment is associated witha change in the molecular charge distribution whichcan be visualized with molecular electrostatic poten-tial (MEP) maps. When a charged particle comes inthe vicinity of a molecule, the charge cloud generatedthrough the molecule’s electrons and nuclei may serveas a guide to assess the molecule’s reactivity towardspositively or negatively charged particle. Thus, theelectrostatic potential maps can be used as an effectivetool to accurately analyze the charge distribution of amolecule and correlate molecular properties like dipolemoments, nucleophilic and electrophilic site and reac-tivity of the molecule towards charged reactants [25].The optimized structural parameters are used toplot the MEP for SO and SO − ground states as shown issociative electron attachment to sulfur dioxide : A theoretical approach and (b) SO − ion both showingthe C v symmetry. The red arrow denotes the directionof the dipole moment for both the cases.in Fig. 4(a) and Fig. 4(b), respectively. The red inthe colour spectrum denotes lowest electrostatic po-tential value while the blue denotes the highest. Thecolour spectrum ranges from -0.271 a.u. (deepest red)to +0.271 a.u. (deepest blue) in both the figures (Fig.4(a) and Fig. 4(b)). It can be observed from Fig. 4(a)that the region of lowest electrostatic potential energy,characterized by abundance of electrons, occurs nearthe bottom O-atoms which is in accordance with theLewis structure (Fig. 1) and also in well agreementwith the MEP reported by Esrafili and Vakili [7]. FromFig. 4(b) it can be observed that after the attachmentof the low-energy electron with the SO molecule, theMEP map of SO − shifts towards higher electron den-sity. But the region of lowest electrostatic potentialstill remains near the O-atoms. This points to the factthat although the electron gets attracted towards theelectro-positive S-atom, it quickly gets transfered tothe O-atoms. The TNI retains the C v symmetry likeits neutral ground state and the dipole moment vectorcan be identified to be pointing downwards in both thecases (Fig. 3(a) and Fig. 3(b)).The bonding features between the incoming elec-tron and the neutral SO molecule can be investigatedand the MEP can be quantified with the help of natu-ral bond orbitals (NBO) analysis. The NBO 3.0 anal-ysis, inbuilt within Gaussian 09 program package, hasbeen carried out to observe the stabilization energiesfor donor-to-acceptor interactions. The NBO calcula-tions for the SO ground state show that the top S-atom (labeled S (1) in Fig. 5(a)) contains a single lone Figure 4: Electrostatic potential maps at 0.001electron/Bohr isodensity surface of: (a) SO molecule,(b)SO − ion. The red in the color spectrum denoteslowest electrostatic potential value while the bluedenotes the highest. The yellow sphere represents theS-atom and the red spheres represent the O-atoms.pair of electrons with an occupancy of 1.993. Whilethe two bottom O-atoms (labeled O (2) and O (3) inFig. 5(a), respectively) share three and two lone elec-tron pairs each thus having a more electro-negativityas compared to the S-atom. The O-atom having threelone electron pairs (O (2) ) is observed with occupanciesof 1.994, 1.843 and 1.545, respectively. Whereas, theother O-atom with two lone electron pairs (O (3) ) hasoccupancies of 1.994 and 1.843 for the first and sec-ond lone pairs, respectively. Second order perturba-tion energy calculated for the lone pair of O (2) and π ∗ bond orbital of S (1) -O (3) ( n → π ∗ ) interaction is 23.68kcal/mol (Fig. 5(a)). Since the σ electrons form themolecular backbone, these electrons are tightly bound.The second order perturbation correction suggests thatthe n → σ ∗ interaction energy between the lone pair ofO (2) and σ ∗ bond orbital of S (1) -O (3) is 76.84 kcal/molwhich is more than the n → π ∗ interaction. Thus the n → π ∗ interaction is energetically favorable.As a low-energy electron gets attached to the neu-tral molecule forming the TNI SO − , the charge distri-bution of the molecule completely changes as predictedby the NBO calculations. NBO calculations for theSO − ground state show that the top S (1) -atom con-tains a single lone pair of electrons with an occupancyof 1.998. While the two bottom O (2) and O (3) atomsshare three lone electron pairs each thus having a moreelectro-negativity as compared to the S (1) -atom (Fig.5(b)). The O (2) and O (3) atoms each have occupan- issociative electron attachment to sulfur dioxide : A theoretical approach σ ∗ and π ∗ orbitals with corresponding labels from NBO analysisfor (a) neutral SO molecule; (b) SO − ion. The smallblack dots denote the lone-pair electrons.cies of 1.995, 1.983 and 1.851 for the three lone pairs,respectively. Second order perturbation energy calcu-lated for the n → σ ∗ interaction of second lone pair ofO (2) and σ ∗ bond orbital of S (1) -O (3) is 13.81 kcal/molbecause there is no π ∗ orbital for SO − ground state(Fig. 5(b)). The second order perturbation energydifference of 9.87 kcal/mol (23.68 - 13.81 kcal/mol) be-tween the n → π ∗ for SO and n → σ ∗ for SO − inter-action suggests that the stabilization energy for SO − is much less than that for neutral SO . Thus, due todonor-acceptor interaction, SO − ground state is morestable than the SO ground state. This is also evidentfrom the HOMO-LUMO gap (5.12 eV for neutral SO and 2.78 eV for SO − ).The NBO density plot for SO and SO − has beenshown in Fig. 6. Initially, for the ground state of SO there is significant overlap between the lone pair of O (2) and π ∗ bond orbital of S (1) -O (3) (Fig. 6(a)). Since thesingle electron gets attached to the neutral SO in up-spin state ( α state), the NBO density plot representingthe β orbital of n → σ ∗ interaction remains unchanged(Fig. 6(c)). The presence of the α spin results in anextra overlap in the same LUMO orbital representedby the n → σ ∗ interaction solely due the extra elec-tron. This can be observed from the NBO density plotfor SO − alpha orbital (Fig. 6(b)). The resultant NBOdensity plot for SO − gives the orbital plot for a to-tal sum of α and β orbitals (Fig. 6(d)). Comparingthe resultant NBO density plot for SO − to that forSO neutral state, it can be seen that there is a muchhigher overlap in the anionic state than the neutral state. This higher overlap again implies the lower in-teraction energy as predicted by the NBO calculations.It can be noted from Fig. 3 that the optimized groundFigure 6: The NBO density plot for SO and SO − molecule. (a) Orbital density plot for SO moleculerepresenting the n → π ∗ interaction. (b) Orbitaldensity plot for SO − molecule representing the n → σ ∗ interaction ( α orbital). (c) Orbital density plot forSO − molecule representing the n → σ ∗ interaction ( β orbital). (d) Orbital density plot for SO − moleculerepresenting the n → σ ∗ interaction ( α and β orbitals).state configuration for the neutral SO (Fig. 3(a)) andTNI SO − (Fig. 3(b)) are not identical. This changein the bond S-O length and O-S-O bond angle can bedetermined from the change in bond order using thefollowing formula:Bond Order= B e + A e B e and A e denotes number of bonding electronsand number of anti-bonding electrons, respectively.The bond order calculated using the bonding andanti-bonding electrons from the NBO analysis (relevantto Fig. 5) are given in Table 1. As can be noted fromFig. 5(a), the resonating single S (1) -O (2) and doubleS (1) -O (3) bonds correspond to bond orders of 0.9 and1.9, respectively. This means, for the optimized groundstate configuration where the lone pairs of electrons re-distribute themselves forming two double bonds (as inFig. 3(a)), the bond orders will be 1.403. This resultmatches well with Grabowsky et al. with an error of6.47% who reported the bond order of sulfur dioxideto be ∼ (1) -O (2) andS (1) -O (3) double bonds. This decrease in the strengthof the bond accounts for the elongation in the bond inFig. 3(b). issociative electron attachment to sulfur dioxide : A theoretical approach ground state S(1)-O(2) 0.903 ∼ ∼ − ground state S(1)-O(2) 0.473 -S(1)-O(3) 0.473 -
4. Vibration spectral analysis
The main objective of computing the vibration spec-tra of the neutral SO and the TNI SO − was to findout the vibration modes connected with the molecularstructure. This in turn, helps to identify the modes re-sponsible for the production of negative fragment ionsfrom the TNI and also note the change in the spec-tra of the negatively charged molecular ion from theneutral parent molecule (Fig. 7). When the frequencyof radiation matches exactly with the vibration fre-quency of the molecule, absorption of radiation takesplace. Thus, the peaks in the IR spectra denote vi-bration modes at respective peak positions based onthe wave number predicted theoretically by the den-sity functional B3LYP/aug-cc-pVQZ method [6]. Theanalysis of the vibration spectra was done with the op-timized structures of SO and SO − . The three vibra-tional frequencies for neutral SO was computed to be1167.96 (symmetric stretching, ν ), 519.22 (symmetricbending, ν ) and 1357.28 (asymmetric stretching, ν )cm − respectively. While the same for SO − was com-puted to be 979.51 ( ν ), 452.23 ( ν ) and 1071.95 ( ν )cm − respectively, as shown in Fig. 8. The vibrationalfrequencies of the three normal modes of vibration forsulfur dioxide were recorded experimentally by Shel-ton et al. using an infrared prism-grating spectrome-ter [3]. The first ( ν ) and third ( ν ) modes both withan A symmetry were observed at 1151.38 and 1361.76cm − , respectively. While the second mode ( ν ) witha B symmetry was observed at 517.69 cm − . A. Gor-don Briggs also reported the vibrational frequenciesof SO using double-beam infrared spectrometer fittedwith a diffraction grating or NaCl prism to be at 1153( ν ), 508 ( ν ) and 1362 cm − ( ν ) [27]. Thus the com-puted vibrational frequencies of the present work forSO matches excellently with literature [3, 27]. But noexperimental or theoretical data detailing the vibra-tional frequencies for SO − has been reported till now.The frequencies for the three modes for SO − are muchless as compared to the frequencies for the three modesfor SO . The change in peak positions for the two be-fore said structures corresponding to different vibrationmodes are shown in Table 2.As can be inferred from Fig. 8, the simultane- ous presence of the symmetric stretching and bendingmodes will give rise to S − fragment formation. As thestretching may produce S − , it has to be followed by thebending mode such that the O-atoms can come closeenough to form O . The same may also produce O − .The two pathways can be written as: SO + e − −→ SO −∗ −→ ( S − + O O − + S (2)The electron affinity of O − and S − beingEA(O )=0.451 eV and EA(S)=2.077 eV, cross-sectionof S − fragment production is much higher than O − [15]. Whereas, the antisymmetric stretching mode mayresult in the formation of O − and SO − negative ionsgive by the following equations: SO + e − −→ SO −∗ −→ ( O − + SOSO − + O (3)The electron affinity of O − and SO − beingEA(O)=1.462 eV and EA(SO)=1.125 eV, cross-sectionof O − fragment production is slightly higher than SO − but both are observed [15]. This observation is in goodagreement with that reported by Gope et al. [14].
5. Potential energy curves and chargedistribution analysis
The potential energy plots with positive adiabaticelectron affinity for SO and SO − ground states havebeen shown in Fig. 9 and Fig. 10 for the followingdissociation pathways: SO −→ ( O + SOS + O (4) SO + e − −→ SO − −→ ( O − + SOS − + O (5) issociative electron attachment to sulfur dioxide : A theoretical approach and SO − anion.Calculated Ref [3] Ref [27](cm − ) (cm − ) (cm − )DFT Calculation ν ν ν ν − anion ν ν
400 600 800 1000 1200Frequency (cm -1 )020040060080010001200 A b s o r p t i o n c o e ff i c i e n t( ε ) SO SO Figure 7: Computed IR spectrum showing differentvibration modes for optimized ground state geometryof SO molecule (blue solid line) and SO − ion (red solidline).Figure 8: Depiction of computed vibration modesfor SO − molecule.The yellow sphere represents the S-atom and the red spheres represent the O-atoms. (a)and (b) represent symmetric stretching mode; (c) and(d) represent symmetric bending mode; (e) and (f)represent anti-symmetric stretching mode. The darkyellow arrow denotes the dipole derivative unit vectorin all the cases.where the B3LYP correlational functional has beenused with the aug-cc-pVDZ basis set. To explore thepotential energy curves for SO and SO − optimized ground state geometries for the two dissociation path-ways given by Eqns. 4 and 5, we investigated thetransition states and scanned over the bond distanceskeeping the transition states of SO and SO − as theinitial geometry in two different ways. In the first cal-culation, the two O-atoms are brought closer from itsequilibrium value (denoted by r in Fig. 9) and theenergy is scanned. This results in the formation of O and S fragments from SO while, S − and O fragmentsfrom SO − . The resulting potential energy curves forSO and SO − optimized ground state geometries areshown in Fig. 9.In the second case, keeping one S-O bond and O-S-O angle fixed, the other S-O is stretched from itsequilibrium value (denoted by r in Fig. 10). This re-sults in the formation of SO and O fragments from SO while, O − and SO fragments from SO − . The resultingpotential energy curves for SO and SO − optimizedground state geometries are shown in Fig. 10. r (Å)1.5 2 2.5 3 3.5 E ne r g y ( e V ) -1012345678 SO ground stateSO ground state r =2.53År =2.66Å Figure 9: Variation of potential energy of SO (bluesolid line) and SO − (red solid line) ground states withO-O bond distance. r denotes the equilibrium O-Obond distance in both the curves.The DFT calculations predict the potential energy issociative electron attachment to sulfur dioxide : A theoretical approach r S-0 ( Å)1 1.5 2 2.5 3 3.5 E ne r g y ( e V ) SO ground stateSO ground state r =1.44År =1.52Å Figure 10: Variation of potential energy of SO (bluesolid line) and SO − (red solid line) ground states withS-O bond distance. r denotes the equilibrium S-Obond distance in both the curves.curves of optimized ground state of SO − to be at alower energy than its neutral parent SO , signifyingthe positive electron affinity of SO . But no SO − can be observed experimentally to form at around -1.4 eV. This can be understood with the followingexplanations. As can be noticed from the potentialenergy curves in Fig. 9 and Fig. 10, there is nocrossing of the SO and SO − curves in the Franck-Condon region. Thus this resonant transition of SO toSO − is not possible. One more reason for not observingany SO − formation at around -1.4 eV could be anextremely small lifetime of the SO − state, as comparedto the time-of-flight which is in the order of ∼ µs [13]. The schematic potential energy curves shownin Fig. 11 depicts the actual SO −∗ states observedexperimentally forming the two resonant peaks at 5.2and 7.5 eV, respectively [13]. While, the SO andSO − ground state curves are computed curves for S-O bond distance variation. The energy values forvertical transition within the Franck Condon regionare calculated from TDDFT calculations and matchexcellently well with the experimental values reportedby Jana and Nandi [13]. However, one can use theequation-of-motion coupled cluster (EOMCC) methodto compute the potential energy curves for excitedstates of the TNI, which is beyond the scope of thiswork.The charge distribution of neutral SO with equi-librium S-O and O-O bond distances of 1.44 ˚ A and2.53 ˚ A respectively, is shown in Fig. 12(a), computedusing Mulliken charge analysis. Mulliken charges aremathematical constructions that have no relation tophysical charges. But it can be used to predict thedistribution of charges within the individual atomsforming the molecule before and after dissociation. r( Å)1 1.5 2 2.5 3 3.5 E ne r g y ( e V ) F r a n c k C o n do n r eg i o n EA(SO2)
Figure 11: The curve for SO (blue solid line) and SO − ground state (red solid line) are computed curves forS-O bond distance variation. While, the SO −∗ for thefirst resonant peak at 5.2 eV (black dashed line) andSO −∗ for the second resonant peak at 7.5 eV (blackdotted line) are schematic potential energy curves. D signifies the dissociation limit.The total atomic charges add up to give the neutralSO molecule although, the S-atom is highly electro-positive and the O-atoms are highly electro-negative.As the S-O bond distance is slowly increased, at somevalue of the S-O bond coordinate the bond rupturesgiving SO and O neutral fragments (Fig. 12(b)). Thisvalue of the bond was computed to be 2.44 ˚ A . From theMulliken charge analysis it can be observed that boththe electro-positivity of the S-atom and the electro-negativity of the O-atoms has decreased in Fig. 12(b)as compared to 12(a), predicting the neutral natureof the fragments. Similarly, with the decrease in O-O bond length, S and O neutral fragments can beobserved to form with 1.13 ˚ A O-O bond length (Fig.12(c)).The SO − anionic ground state charge distributionis shown in Fig. 13(a) with S-O and O-O equilibriumbond distances as 1.52 ˚ A and 2.66 ˚ A , respectively. Thetotal charge of this anionic system can be observedto add up -1 unit of electronic charge, signifying theattached low-energy electron. As the S-O bond isgradually stretched, SO and O − fragment formationcan be seen at S-O bond distance of 1.82 ˚ A (Fig. 13(b)).The charge distribution predicts the SO fragment to bealmost neutral, while the O − fragment carries most ofthe negative charge. Whereas, gradual decrease in O-O bond distance results in the formation of S − and O fragments, with O-O bond length being 1.21 ˚ A (Fig.13(c)) which matches excellently with the 1.21 ˚ A bondlength of molecular oxygen. issociative electron attachment to sulfur dioxide : A theoretical approach molecule; (b)dissociation of the neutral molecule into SO and Ofragments; (c) dissociation of the neutral molecule intoS and O fragments. The yellow sphere denotes S-atomand red spheres denote O-atoms.Figure 13: Schematic showing Mulliken chargedistribution for (a) TNI SO − ; (b) dissociation of theanion into SO and O − fragments; (c) dissociation ofthe anion into S − and O fragments. The yellow spheredenotes S-atom and red spheres denote O-atoms. Theblue shaded cloud represents electron cloud.
6. Symmetry states of the TNI
In order to get an idea about the symmetry states fa-vorable for DEA to SO molecule, the optimized ge-ometries were then used to carry out time-dependentdensity functional theory (TD-DFT) calculations andget the vertical energy values and symmetries of cor-responding excited states for the SO − molecule lyingwithin the Franck Condon region. Then the symmetrystates lying near the resonant peaks (first resonance observed in the range 4.6 - 5.6 eV and second reso-nance observed in the range 7.0 - 7.6 eV by differentgroups [1, 8, 13]) and having symmetries with consid-erable value of oscillator strength (f) are noted (Fig.11). To check the validity of the calculations, the sym-metries are then compared with reported experimentaland theoretical data.In TDDFT calculations, oscillator strength (f) de-notes the probability of transition between energy lev-els in an atom or molecule with the help of absorptionor emission of electromagnetic radiation. Thus a highoscillator strength for a specific transition would meanthat particular transition is more probable than theothers. The table showing the symmetry states for thetwo resonances with considerable f-value are shown inTable 3 in order of descending f-value.As can be noted from the Table 3, in the energyrange 4.6 - 5.6 eV, the state having the highest oscil-lator strength is an A state with f = 0.0515. AnotherB state can also be observed in the considered energyrange but with very low oscillator strength and hencecan be neglected. No other symmetry states were foundin this energy range with considerable f-value (almost7.2 times less than 0.05). Thus the computation pre-dicts that the first resonant peak due to DEA to SO results from an A negative ion resonant state. Thismatches excellently with previous reports [1, 8, 13].For the second resonance, negative ion resonantstates lying in the energy range 7.0 - 7.6 eV with con-siderable f - value can be assumed to have a contribu-tion. Six symmetry states can be observed with highf-values and are reported in Table 3. Amongst these,four are B and two are A symmetry states. Fromthis observation, it can be concluded that the secondresonance occurs due to an A to A + B transition.This result matches excellently with the recent exper-imental work on DEA to SO by Jana and Nandi [13].For all the basis sets used, the oscillator strengths ofA negative ion states are always 0. This supports thefact that if the initial state of the neutral is an A , thenA to A transition is always forbidden [1].
7. Conclusion
The theoretical and computational approach helps tovisualize the attachment of a single low-energy ( ≤ molecule thus formingthe molecular anion SO − . The molecular sites actingas positive centers to the incoming electron couldbe identified using the MEP of the neutral moleculeand the results are in well agreement with the MEP issociative electron attachment to sulfur dioxide : A theoretical approach from TD-DFT calculations with SO − ground state optimized geometrywith the aug-cc-pVQZ basis and B3LYP exchange-correlational functional.Resonance Energy Symmetry Oscillator Ref [13]range (eV) of TNI strength (f)First 4.5 - 5.8 eV A Peak B + B B molecule. The negative ionresonant states responsible for the two resonant peakshave also been identified with the help of TD-DFTcalculations to the optimized ground state geometriesas A for the first resonance and A +B for the secondresonance, respectively. The results match excellentlywith that reported experimentally from DEA to SO by Jana and Nandi [13].
8. Acknowledgments
We gratefully acknowledge financial supports fromScience and Engineering Research Board (SERB)for supporting this research under the ProjectEMR/2014/000457 and for computational facility un-der the Project SB/FTP/CS-164/2013.
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