Influence of Isotope Effects on Product Polarizations of N( 2 D)+D 2, N( 2 D)+H 2 and N( 2 D)+HD Reactive Systems

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1 CHEM. RES. CHINESE UNIVERSITIES 202, 28(5), Influence of Isotope Effects on Product Polarizations of N( 2 D)+D 2, N( 2 D)+H 2 and N( 2 D)+HD Reactive Systems NIE Shan-shan and CHU Tian-shu,2*. State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 6023, P. R. China; 2. Institute for Computational Sciences and Engineering, Laboratory of New Fiber Materials and Modern Textile, the Growing Base for State Key Laboratory, Qingdao University, Qingdao 26607, P. R. China Abstract To figure out the influence of isotope effect on product polarizations of the N( 2 D)+D 2 reactive system and its isotope variants, quasi-classical trajectory(qct) calculation was performed on Ho s potential energy surface(pes) of 2 A state. Product polarizations such as product distributions of P(θ r ), P(φ r ) and P(θ r,φ r ), as well as the generalized polarization-dependent differential cross sections(pddcss) were discussed and compared in detail among the four product channels of the title reactions. Both the intermolecular and intramolecular isotope effects were proved to be influential on product polarizations. Keywords Isotope effect; Product polarization; Quasi-classical trajectory calculation; Potential energy surface Article ID (202) Introduction Stereo-dynamics, namely the three-dimensional molecular movement and the product spatial orientation and alignment, plays a vital role in chemical reactions []. In recent years, a lot of theoretical calculations and experimental techniques have been implemented and continuously improved in order to understand fully the stereo-dynamics of chemical reactions [2 5]. As a prototype of insertion reaction, the NH 2 reactive system has been studied for decades [6 ] because of its important role in atmospheric chemistry and combustion process [2]. Although tremendous researches on inetics features and chemical stereo-dynamics of the title reactions have been involved on the ground and excited electronic states( 4 S, 2 D and 2 P states) of the nitrogen atoms [6,3 5], the major interests are, however, focused on the first excited state nitrogen atoms, N( 2 D), which are more reactive than the ground state N( 4 S) atoms. The conception of isotope effect is raised out [6] because it often plays an important role in probing and analyzing the mechanisms of chemical reactions [7 9], and since Chen et al. [20] investigated the isotope effect in stereo-dynamics for the Cl+H 2, D 2 and HD reactions, it can no longer be neglected in chemical dynamics studies [2 24]. In this paper, we emphasize on the influence of isotope effects on product polarizations for the title reactions involving the lowest N( 2 D) excited state. And we mainly discussed the two inds of isotope effects, that is, the intermolecular isotope effect between the N( 2 D)+D 2 and the N( 2 D)+H 2 reactions, and the intramolecular effect between the two product channels of the N( 2 D)+HD reaction. The quasi-classical trajectory(qct) calculation was performed on Ho s potential energy surface (PES) [25 27], which is a globally smooth PES for the ground state( 2 A state) of the N( 2 D)+H 2 reaction and is based on ab initio points resulted from the multi-reference configuration interaction(mrci) calculations. With respect to the influence of the two isotope effects, all the QCT calculated results were discussed in detail, including polarization-dependent differential cross sections(pddcss), as well as the P(θ r ), P(φ r ) and P(θ r,φ r ) angular distributions. The paper describes the calculation aspects carried out in the present wor, clarifies the results and discussions gained from the present wor and gathers the concluding remars. 2 Theory and Calculations In the present wor, we employed the QCT calculation used in former stereo-dynamic studies [28 38]. The QCT calculation was carried out via a center-of-mass(cm) frame(see Fig.) with the reagent relative velocity vector parallel to the z-axis, and the initial and final relative velocity vectors, and contained in the x-z scattering plane [39]. Fig. Center-of-mass coordinate system used to describe the vector properties *Corresponding author. tschu@dicp.ac.cn; tschu008@63.com Received December 8, 20; accepted December 29, 20 Supported by the National Natural Science Foundation of China(No ).

2 898 CHEM. RES. CHINESE UNIVERSITIES Vol.28 Vector correlations can be expanded in a series of Legendre polynomials. In detail, the angular distribution of P(θ r ) describes the -j correlation, which can be written as P( θr) = (2+ ) a0 P(cos θr) () 2 The coefficients a 0 = P (cosθ r ) are defined as orientation ( is odd) or alignment( is even) parameters. The dihedral angle distribution of P(φ r ) describes the - -j correlation and can be expanded as Fourier series, P( φr) = [+ ancos( nϕr) + bnsin( nϕr)] (2) 2π n(even 2) n(odd ) where an = 2cosnφ, r bn = 2 sinnφ. r The joint probability density distribution of P(θ r,φ r ) is expressed by P( θr, ϕr) = ( aq± cosqϕr aq isin qϕr) Cq( θr,0) (3) 4π with a q ± given by q 0 ( θ ) a = ± 2 C,0 cosqφ ( is even) (4) q q r r ( θ ) a = 2 i C,0 sinqφ ( is odd) (5) q q r r Presented by a set of generalized PDDCSs, the full three-dimensional angular distribution can be written as the sum [39,40], [ ] dσ q * P( ωt, ωr) = Cq( θr, ϕr) q 4πσ dω (6) t where []=2+, (/σ)(dσ q /dω t ) are the generalized polarization parameters that describe the anisotropic features of angular momentum distribution, and C q (θ r,φ r ) are simply expectation values of the appropriate modified spherical harmonic. The PDDCSs can be further written as d σ q± [ ] = S q C (,0) q θ (7) ± t σ dωt 4π with given as S q ± q iqϕr iqϕr Sq± = c (,0) (,0) ( ) e e q θt cq θ r ± (8) In this study, the product polarization distributions for NH 2 reactive system and its isotope variants have been investigated by QCT calculation performed on Ho s PES [27] at the collision energy of 67.4 J/mol, and batches of trajectories were sampled for each reaction. The reason why we chose a collision energy of 67.4 J/mol(.74 ev) is to ensure an easy occurrence of the reaction process and thus saves the computational time for performing the present QCT calculation. The initial distance from the N( 2 D) atoms to the center of the mass of the D 2 /H 2 /HD molecules is.0 nm, with the initial rovibrational values of v=0, j=0. The integration step was chosen to be 0. fs. 3 Results and Discussions 3. Influence of Isotope Effects on the Distributions of P(θ r ), P(φ r ) and P(θ r, φ r ) The angular distribution of P(θ r ) reflects the j - vector correlation, while the dihedral angle distribution of P(φ r ) describes the - -j vector correlation. As seen, Fig.2(A) displays P(θ r ) distributions with all peas at 90, and they are symmetric with respect to 90. That is to say, for the N( 2 D)+D 2, N( 2 D)+H 2 and N( 2 D)+HD reactions, the product rotational angular momentum j tends to be aligned along the direction perpendicular to. In Fig.2(B), each reaction displays the P(φ r ) distribution asymmetric with respect to the - scattering plane, directly indicating that the product rotational angular momentum j has orientation. The polar plots of P(θ r,φ r ) distribution for the title reactions are shown in Fig.3, which represent the scattering angle average of the full distribution of P(ω t,ω r ). Peaing at (90,90 ) and (90,270 ), the P(θ r,φ r ) distributions are in good agreement with the P(θ r ) and P(φ r ) distributions. This indicates that the product molecules prefer to polarize in the orientation perpendicular to the scattering plane, and the four reactions are dominated by the in-plane mechanism [2]. Despite the common features illustrated by these angular distributions, we will present and discuss the differences among them for the purpose of the investigation of the influence of isotope effects. Fig.2 Product polarization distributions calculated on Ho s potential energy surface at a collision energy of 67.4 J/mol for the N( 2 D)+D 2 reactive system and its isotope variants (A) The angular distribution of P(θ r ) as a function of θ r between and j over a range of 0 80 ; (B) the dihedral angular distribution of P(φ r ) as a function of the dihedral angle φ r in a range of a. The reaction of N( 2 D)+D 2 ; b. the reaction of N( 2 D)+H 2 ; c. the NH+D product channel of the N( 2 D)+HD reaction; d. the ND+H product channel of the N( 2 D)+HD reaction Influence of the Intermolecular Isotope Effect on the Distributions Between the N( 2 D)+H 2 and N( 2 D)+D 2 Reactions With respect to the intermolecular isotope effect, the N( 2 D)+H 2 reaction exhibits a higher and narrower P(θ r ) distribution in contrast to that of the N( 2 D)+D 2 reaction in Fig.2(A), which shows a stronger product alignment of the N( 2 D)+H 2 reaction. In previous studies, Han and coworers [2,33] analyzed the product polarization of the reactions for different mass

3 No.5 NIE Shan-shan et al. 899 Fig.3 Jointed probability density distribution of P(θ r,φ r ) as a function of both θ r in a range of 0 80 and φ r in a range of for different reactive systems (A) N( 2 D)+D 2 ND+D; (B) N( 2 D)+H 2 NH+H; (C) N( 2 D)+HD NH+D; (D) N( 2 D)+HD ND+H. combinations. They proved that the product rotational angular momentum j was extremely sensitive to the mass factor cos 2 β [cos 2 β=m A m C /(m A +m B )(m B +m C ) for the tri-atomic reaction of A+BC AB+C], which was notable for the anisotropic features of the HHL, LLL, HLL and LHL mass combination reactions(h: heavy; L: light). In this paper, the calculated mass factors for the investigated reactions are listed in Table. For the NH 2 and ND 2 reactive systems, we can see that with the increase of the mass factor cos 2 β, the product rotational alignment parameter P 2 (j ) becomes more negative, which means that the larger mass factor enhances the anisotropic distribution of j with respect to. This tendency is in good agreement with the P(θ r ) distributions of the N( 2 D)+H 2 and N( 2 D)+D 2 reactions. Besides, each P(φ r ) distribution in Fig.2(B) shows a higher pea at φ r =90, representing a preferred orientation with the right-handed product rotation confining in planes parallel to the - scattering plane [2]. Table Average values of the product rotational alignment parameters P 2 (j ) and the mass factor cos 2 β calculated at a collision energy of 67.4 J/mol for the N( 2 D)+D 2 reactive system and the isotope variants System P 2 (j ) cos 2 β N( 2 D)+D 2 ND+D N( 2 D)+H 2 NH+H N( 2 D)+HD NH+D N( 2 D)+HD ND+H It can be clearly seen that the higher and narrower P(φ r ) distribution of the N( 2 D)+H 2 reaction implies that the product polarization is stronger in the N( 2 D)+H 2 reaction than in the N( 2 D)+D 2 reaction. Thus, it is reasonable to believe that the larger mass factor, of the NH 2 reactive system, intensifies the degree of product polarization. Moreover, the polar plots of P(θ r,φ r ) distributions in Fig.3(A) and (B) show both peas at (90,90 ), which are in good agreement with the P(θ r ) and P(φ r ) distributions of the two reactions. Actually, the fact that the P(φ r ) distribution is asymmetric with respect to φ r =80, while the P(θ r ) distribution is symmetric about θ r =90 can be explained by the impulse model [28]. In the A+BC AB+C tri-atomic reaction, the product rotational angular momentum can be written as j =Lsin 2 β+jcos 2 β+ J m B /m AB, where L and J are orbital and rotational angular momenta for the reagents, and J =(μ BC R) /2 (r AB r CB ). In this equation, μ BC refers to the reduced mass of the BC molecule; r AB and r CB are the unit vectors where atom B points to A and C, respectively; R is the repulsive energy. Based on this model, for the specific NH 2 reactive system, the symmetric term of Lsin 2 β+jcos 2 β and the asymmetric term of J m B /m AB play a role in the chemical bond breaing and forming, and thus, the reason that causes the biased product orientation should be the repulsive energy R embedded in the latter term of J m B /m AB. In Fig.2(B), the degree of the P(φ r ) asymmetry is greater in the N( 2 D)+H 2 reaction than in the N( 2 D)+D 2 reaction. According to the impulse model, it is possible that the former reaction has a larger repulsive energy R, thus leading to the greater degree of the P(φ r ) asymmetry. Since the mass factor is larger in the N( 2 D)+H 2 reaction than in the N( 2 D)+D 2 reaction, we can infer that the impulse energy R might increase with increasing the mass factor cos 2 β, giving rise to a greater degree of the P(φ r ) asymmetry in the context of the intermolecular isotope effect Influence of Intramolecular Isotope Effect on the Distributions of the N( 2 D)+HD Reaction As far as the intramolecular isotope effect is concerned, the higher and narrower angular distribution of P(θ r ) of the NH+D channel in Fig.2(A) presents a stronger product alignment than that of the ND+H channel. This observed feature may be attributed to their different product rotational alignment parameters P 2 (j ) and mass factors cos 2 β, that are and in the NH+D channel and

4 900 CHEM. RES. CHINESE UNIVERSITIES Vol and in the ND+H channel, respectively(see in Table ). The P 2 (j ) values are closer to each other with increasing cos 2 β, yet the higher and narrower P(θ r ) distributions of the NH+D channel in Fig.2(A) indicates that the larger the mass factor, the stronger the product alignment perpendicular to. From the P(φ r ) distributions of the two product channels for the N( 2 D)+HD reaction in Fig.2(B), we can see that the preferred product rotational direction in the NH+D channel is left-handed(distribution pea higher at φ r =270 ), while in the ND+H channel, the preferred product rotational direction is right-handed (distribution pea higher at φ r =90 ). These differences in product alignment or orientation can be explained by the impulse model raised in Section 3.., in which the impulsive energy R leads to the preferred product rotational direction of the NH or ND molecules. Fig.3(C) and (D) depict the polar plots of the P(θ r,φ r ) distributions of the NH+D and ND+H channels peaing at (90,270 ) and (90,90 ), respectively, which are in good accordance to their P(θ r ) and P(φ r ) distributions. These P(θ r,φ r ) distributions suggest that the products are preferentially polarized in the direction perpendicular to the - scattering plane and the reaction is dominated by in-plane mechanism at a collision energy of 67.4 J/mol despite the intramolecular isotope effect. To draw a conclusion, at a fixed collision energy of 67.4 J/mol, it is common for the investigated reactions that increasing mass factor cos 2 β enhances the product alignments and orientations concerning both the intermolecular and the intramolecular isotope effects. This is consistent with the investigation of the ground-state N( 4 S) atoms reacting with H 2 and its isotopic variants of Zhang et al. [24]. Besides, as compared to that of the N( 2 D)+D 2 reaction, the product rotational orientation of the N( 2 D)+H 2 reaction is reinforced due to the intermolecular isotope effect, whereas the two product channels of the N( 2 D)+HD reaction have their own preferred product rotational directions because of the intramolecular isotope effect. 3.2 Influence of Isotope Effect on Product Polarizations The PDDCSs calculated at an investigated collision energy of 67.4 J/mol for the N( 2 D)+D 2, N( 2 D)+H 2 and N( 2 D)+HD reactions are shown in Fig.4. They provide rich dynamic information [34,39] about the rotational polarization of the reaction product and its CM scattering angle dependence. The =0, q=0 PDDCS, (2π/σ)(dσ 00 /dω t ), describing the - vector correlation, is proportional to the normal differential cross-section(dcs). All the (2π/σ)(dσ 00 /dω t ) distributions in Fig.4(A) are broad and appear to pea at the two extreme scattering angles 0 and 80. The =2, q=0 PDDCS, (2π/σ) (dσ 20 /dω t ), is the expectation value of the second Legendre moment P 2 (cosθ r ) [5,28]. As seen in Fig.4(B), the (2π/σ) (dσ 20 /dω t ) distributions show an opposite trend compared with the (2π/σ)(dσ 00 /dω t ) distributions, which means that the product rotational angular momentum j aligns along the direction perpendicular to. Away from these extreme scattering angles, all the =2, q=0 PDDCSs become close to zero, suggesting that the rotational angular momentum distributions in cosθ r for these investigated reactions are more isotropic for sideways scattering. For the purpose of thoroughly understanding the degree of product polarizations, we compared the calculated =2, q=0 PDDCSs to the limiting values listed in Table 2(see more detailed discussion below). The other two =2, q 0 PDDCSs, (2π/σ)(dσ 22+ /dω t ) and (2π/σ)(dσ 2 /dω t ), are shown in Fig.4(C) and (D). The expectation values of these =2, q=2+ and =2, q= moments Fig.4 Polarization-dependent differential cross sections as a function of scattering angle over a range of 0 80 Distribution: (A) (2π/σ)(dσ 00 /dω t ); (B) (2π/σ)(dσ 20 /dω t ); (C) (2π/σ)(dσ 22+ /dω t ); (D) (2π/σ)(dσ 2- /dω t ). a. The reaction of N( 2 D)+D 2 ; b. the reaction of N( 2 D)+H 2 ; c. the NH+D product channel of the N( 2 D)+HD reaction; d. the ND+H product channel of the N( 2 D)+ HD reaction.

5 No.5 NIE Shan-shan et al. 90 Table 2 Arguments and limiting values of the generalized PDDCSs q± a Argument Limiting values b (θ r,φ r ) 0, 0 0, 90 45, 0 45, 90 45, 80 90, 0 90, P 2 (cosθ r ) C 2 (θ r, 0)cosφ r C 22 (θ r, 0)cos2φ r a. The, q index; b. limiting values are listed corresponding to the given(θ r,φ r ) angles. Statistics are determined in ref. [34]. are far from the limiting values given in Table 2, perhaps not surprisingly for the insertion dominated mechanism [34 37] for the title reactions. Note that at those forward and bacward scattering angles, these two PDDCSs are necessarily zero. It is common for these reactions that at these limiting scattering angles, the - scattering plane is not defined and all moments with q 0 must be zero. More interesting is the behavior of the q 0 moments at scattering angles away from the extreme forward and bacward directions, since these provide information on the φ r dihedral angle distribution. Unlie the q=0 PDDCSs, those with q 0 are non-zero at scattering angles away from θ t =0 and 80, clearly indicating that although not strongly polarized, the P(θ r,φ r ) distributions are anisotropic for sideways scattering products of the title reactions(see more detailed discussion below). Despite these discussed common features, the influence of the isotope effects on the distributions of the four PDDCSs for the reactions are different Influence of the Intermolecular Isotope Effect on the Product Polarizations of the Reactions of N( 2 D)+D 2 and N( 2 D)+H 2 First and foremost, the (2π/σ)(dσ 00 /dω t ) distributions of the N( 2 D)+H 2 and N( 2 D)+D 2 reactions in Fig.4(A) both show biased bacward product scatterings which are stronger in the former and weaer in the latter, indicating that the product scattering of the N( 2 D)+H 2 reaction is actually reinforced because of the intermolecular isotope effect. From the previous wor [39], the =2, q=0 PDDCS is proportional to (3cos 2 θ r )/2, and it reaches a limiting value of 0.5 when θ r is getting close to 90. Therefore, the behavior of the =2, q=0 PDDCS at the extreme forward and bacward scattering angles is the indicative of the product alignment perpendicular to. A calculated value of at a scattering angle of 80 for the N( 2 D)+H 2 reaction is larger than that for the N( 2 D)+D 2 reaction, and is so close to a limiting value of 0.5 that the product alignment perpendicular to is extremely strong at the extreme bacward scattering angle for the N( 2 D)+D 2 reaction. Therefore, we might conclude that, between the two reactions of N( 2 D)+H 2 and N( 2 D)+D 2, the larger the mass factor, the stronger the product alignment perpendicular to. This is in accordance with the former P(θ r ) distribution described in Section 3... Besides, the values of the other two q 0 PDDCSs, (2π/σ)(dσ 22+ /dω t ) and (2π/σ)(dσ 2 /dω t ), are shown in Fig.4(C) and (D), respectively. It is clearly seen that the calculated (2π/σ)(dσ 22+ /dω t ) values for the two reactions are less than zero, which proves that both the product molecules align along the y-axis perpendicular to at scattering angles in a range of The phenomenon that the two curves are close to each other at first lead us to believe that the reactions of N( 2 D)+H 2 and N( 2 D)+D 2 might share the same anisotropic features. However, Fig.4(D) shows that the two curves have oscillations at different scattering angles, that is, the product molecules show orientations parallel to (>0) or anti-parallel to (<0) y-axis at different scattering angles. Moreover, the N( 2 D)+H 2 curve shows two more oscillations than the N( 2 D)+D 2 curve, which gives the evidence that the anisotropic feature of the N( 2 D)+H 2 reaction is stronger than the N( 2 D)+D 2 reaction. Thus, the intermolecular isotope effect might reinforce the anisotropic features of the N( 2 D)+D 2 reaction when deuterium is substituted by hydrogen Influence of the Intramolecular Isotope Effect on the Product Polarizations of the N( 2 D)+HD Reaction So far as the N( 2 D)+HD reaction in concerned, it can be clearly seen in Fig.4(A) that the ND+H product channel exhibits a biased bacward scattering, while the NH+D product channel exhibits a forward-bacward scattering. The (2π/σ)(dσ 00 /dω t ) values of the NH+D product channel are smaller than those of the ND+H product channel at the extreme scattering angles. That is to say, with increasing mass factor, both the forward and bacward scattering are weaened, while the degree of the weaened bacward scattering is even greater. In Fig.4(B), neither of the calculated (2π/σ)(dσ 20 /dω t ) curves reaches a limiting value of 0.5, but the product alignments perpendicular to are strong at those forward and bacward scattering angles. Furthermore, a value of for the NH+D curve at a scattering angle of 80 is closer to 0.5 than that for the ND+H curve, evidencing that with increasing mass factor, the product alignment perpendicular to is intensified in consideration of the intramolecular isotope effect. This is consistent with the former P(θ r ) distribution described in Section Then Fig.4(C) and (D) show the curves of =2, q 0 PDDCSs for the two product channels. In Fig.4(C), the less-than-zero (2π/σ)(dσ 22+ /dω t ) values of the two product channels indicate that the product aligns along the y-axis perpendicular to at different scattering angles, whereas the above-zero values of the NH+D channel at scattering angles from 40 to 80 show that a part of its product molecules align along the x-axis perperndicular to. This proves that the larger mass factor leads to a weaer degree of the product alignmet along the y-axis perpendicular to, which results in the stronger anisotropic feactures of the NH+D product channel. Fig.4(D) shows oscillations around zero of the two (2π/σ)(dσ 2 /dω t ) curves at different scattering angles. Those oscillations of the curves reveal that the product molecules orient in the direction parrallel to (>0) or anti-parallel to (<0) y-axis at different scattering angles. Since the NH+D channel ocsillate more firecely than the ND+H channel, we may come to the conclusion that the intramolecular isotope effect

6 902 CHEM. RES. CHINESE UNIVERSITIES Vol.28 enhances the anisotropic feactures of the NH+D product channel. Therefore, influences of both the intermolecular and the intramolecular isotope effects on the product polarizations can be easily seen from these PDDCS distributions. With increasing mass factor, the products show a tendency of stronger forward and bacward scatterings with respect to the intermolecular isotope effect; yet the products display a weaer forward and a stronger bacward scattering in consideration of the intramolecular isotope effect. What s more, for both the intermolecular and the intramolecular isotope effects, it is common that increasing mass factor will enhance the degree of the product alignment perpendicular to as well as the degree of the anisotropic features of these reactions. 4 Conclusions From the above discussions, the following results can be obtained. The larger the mass factor, the stronger the product alignments and orientations in consideration of both the intermolecular and the intramolecular isotope effects. The intermolecular isotope effect results in a stronger product rotational orientation of the H 2 reaction than the D 2 reaction, while the intramolecular isotope effect leads to the two different product rotational directions for the two product channels in the N( 2 D)+HD reaction. For both the intermolecular and the intramolecular isotope effects, increasing mass factor enhances the degree of the product alignment perpendicular to as well as the degree of the anisotropic features of these reactions. 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