Analytical Potential Energy Surface And Dynamics Study Of Polyatomic Reaction System

This dissertation is composed of two parts. One part is the constructions of potentialenergy surfaces (PESs) for He+H₂⁺,He₂+H+and potential energy function for groundΧ1Σ+and excitedÎ’1Πstates of KH molecule. The other part is the dynamics studies of the He+H₂⁺ reaction, H+HBr exchange reaction and He₂+H+by the method of quasi-classical trajectory.The essay can be divided into six charpters. The first two charpters are about the basictheories of the construction of PES and the main concepts of the dynamics reactions. And wediscuss our researches about HeH₂⁺ , He₂H+, H2Br and KH in the last four charpters in detail.In the third charpter, a new PES for the ground electronic state(12A')of the HeH₂⁺ hasbeen constructed by fitting 8840 ab initio points at the MRCI/aug-cc-pV5Z level of theory,using the many-body expansion method with root-mean-square deviation 0.0677 Kcal/mol.Before the energy grids are calculated, we have calculated the energies of the point of(RHeH⁺=2 bohr, RHH+=2 bohr,θ=180o)using different active orbitals. We find that potentialenergy changes little, if active orbitals continue increasing after the active orbitals is set to occ,10, 2. Thus, we choose occ, 10, 2 to define the active orbitals. The total integral reaction crosssections for the reaction of He+H₂⁺ (v=0-3)→HeH⁺+H have also been calculated as afunction of the collision energy in the range of 0-2 eV using the method of quasi-classicaltrajectory. The calculated results are closer to the experiment results than those previousresults indicating the new PES can be based on for the dynamics researches.Second, the reactant - vibration - excitation effect on the abstraction reaction ofH+HeH⁺(ν=0, 1, 2, j = 0)→He+H₂⁺ and exchange reaction H′+HeH⁺(ν=0, 1, 2,j = 0)→HeH′++H are investigated. Both the abstraction reaction H + HeH⁺→H₂⁺ +He andexchange reaction H+HeH⁺→HeH⁺+H are typical ion-molecular reactions sharing the samereactants, however they have different reactive mechanisms. The abstraction reaction has skew angle (β) cos2β=0.3994 in the HH+He mass weighted coordinate system, which isbelonged to light-light-heavy (LLH) model. While the exchange reaction belonges to LHLmodel. The energy distribution, vibrational and rotational distributions of product H₂⁺ andHeH′+are investigated. Due to different inner reactive mechanisms, the three distributions forthe two reactions are much different and vibrational excitation of reactant is more effective tothe exchange reaction than abstraction reaction. The influences of reactant vibrationalexcitation on stereodynamics are also discussed in this paper. The well in the energy path ofabstraction reaction do not have obvious influence on the scattering / alignment / orientationdegrees of abstraction reaction which are much stronger than those of exchange reaction.Third, the vector correlations in the H + HeH⁺/ H + HeD+/ H + HeT+reactions are discussedand the remarkable isotopic effect is revealed.In the fourth chapter, a new PES for the exchange reaction of HeH⁺(X1∑+) + He at thelowest singlet state 11A' has been builted. The APES is expressed as Aguado-Paniagua (AP)function based on the many-body expansion. Using the adaptive nonlinear least-squaresalgorithm, the APES is fitted from 15682 ab initio energy points calculated with themultireference configuration interaction calculation with a large d-aug-cc-pV5Z basis set. Wetest the accuracy of theoretical level by computating the energy gap between the dissociationlimits of the 11A' and 13A' states of He₂^H+system. And the value is the same as the result ofBaccarelli. The spectroscopic constants based on the PECs for the HeH⁺(X1∑+) and He₂+(1²Ã¢Ë†â€˜_u⁺) states are in agreement with the available experiment data in the literature, whichimplies that the present theoretical level is suitable for treating the present system. Tointuitively evaluate the characteristics of the present APES, we plot the minimum energy path(MEP) for the HeH⁺+ He→He + H+He reaction. The new MEP which is very similar to thatof Panda et al near the well range is smoother in the region close to the asymptote of HeH⁺+He. We also present some contour diagrams of the APES at different angles and find that thepresent contour diagrams are similar to those from the APES of Panda except some subtledetails. To testify the new APES, we calculate the integral cross sections for He + H+He (v =0, 1, 2, j = 0)→HeH⁺+ He by means of quasi-classical trajectory and compare them with theprevious result in literature and the QCT and TDQM results are in good agreement especiallyfor v = 1. He' + ^H+He→He'H⁺+ He, which belongs to the heavy-light-heavy (HLH) model, is atypical ion-molecule reaction: the reaction has no threshold and the ICSs decrease rapidly asEcincreases; there is a potential well corresponding to the global minimum of the system indepth of about 0.577 eV along the collinear MEP, which is easy to form the long-livedcomplex. However, Bhattacharya et al.[111]found that instead of a long-lived complexformation, a short-lived intermediate is formed with features closer to a direct reaction. Thefurther analysis of the inner reactive mechanism to form the intermediate is beyond the scopeof their study. In order to explain the inner reactive mechanisms and shed more light on thestate-to-state dynamics, we carry out QCT calculations for He' + H+He (v = 0, j = 0)→He'H++ He at different Ecs to investigate the inner reaction mechanisms. We calculate the reactivetime, energy distribution, vibrational and rotational distributions at different collision energy.And we find that the reaction at Ec= 0.05 eV is mainly governed by indirect reactivemechanism and direct reactive mechanism takes more fraction as Ecincreases. The long-livedcomplexes corresponding to He₂H⁺metastable states in the indirect reactive mechanism areformed during trajectories are trapping by effective deep potential well at low Ec. It is veryinteresting that product He'H⁺mainly focuses onν= 0 at the five Ecwhich is attributed tolarge gap between the lowest two vibrational energy levels for He'H⁺(X¹Ã¢Ë†â€˜⁺).The influences of collision energy on stereodynamic qualities are discussed. In general,stereodynamic qualities of the reactions resemble those investigated by Wang et al. in theHLH model on attractive surface. As Ecincreases from 0.05 eV to 0.5 eV, the productmolecular is mainly forward scattering and rotational angular momentum vectors j′is not onlyaligned along the y-axis and but also oriented along the positive direction of y-axis. As thedirect reactive mechanism is gradually governed the total reaction with the increment of Ec,the degree of scattering / alignment / orientation product becomes more obvious.In the end of the chapter, we discuss the influences of vibrational energy, the rotationalenergy and the isotopic substituted of the reactant molecular on the on vector correlation ofexchange reaction. During calculation, the collision energy is chosen at Ec= 0.2 eV. Theresults indicate that vibrational energy has more influence on the product rotational angularmomentum than isotopic substituted and rotational energy show little effect on productrotational angular momentum. In the fifth chapter, we discuss the impact of the collision energy on the exchangereaction H' + HBr (ν= 0, j = 0)→H + H'Br and we calculate thermal rate as function ofcollision energy for the abstract reaction of H + HBr (ν= 0, j = 0)→H₂⁺ Br.As the Br atom has more electrons and a much heavier mass than F and Cl, the accurateab initio PES for the BrH2system is more difficult to develop. Kurosaki and Takayanagiconstructed global adiabatic PESs of the lowest three doublet states for the BrH2system usingmulti-reference configuration interaction, including Davidson's correction and aug-cc-pVTZand the ground PES is called MB3. There were a lot of dynamics researches based on the PES,however, the stereodynamic investigation for the exchange reaction had not been reported, yet.Therefore, in order to understand the reaction process fully, we performed QCT on the MB3PES.At first, the influence of collision energy on the scar vector is discussed. The crosssections, computed at the collision energies of 0.5–2.0 eV, are in good agreement with thoseof the QM calculations based on the same PES, implying that the quantum effects in theintegral cross section are not significant. The ICS near 0.5 eV is very low because theexchange reaction has a barrier height of about 0.42 eV. Once Ec exceeds the barrier height ofthe reaction, the present ICSs monotonically increase with the growth of Ec, revealing a largeacceptance cone. The rotational, vibrational, and translational fractions in the total energy andthe vibrational distribution for the product molecule are calculated for the exchange reaction.When Ec ranges from 0.5 to 2.0 eV, translational fraction obviously decreases and rotationalfraction obviously increases, but vibrational fraction undergoes a slight change. Althoughdecreasing, translational fraction still occupies the largest fraction of the total energy in theconsidered Ecrange, indicating the repulsive character of the PES. The most populatedvibrational level for each Ecis v = 0, and ICS regularly decreases with v. These findingsreveal the diminution of the open rotational state in a given vibrational manifold.The resultssupport the repulsive character of the PES. We plotted the internuclear distances for all thereaction trajectories at the five Ecand found no indirect reaction, which is ascribed to only abarrier along the reaction process.The alignment and orientation of the product HBr are investigated in detail withstereodynamics. The product is mainly scattered backward, which is related with the repulsive character of the PES and the LHL model. As Ec increases, the trend of backward scatteringbecomes weaker. The product molecular shows the preference of alignment along the y-axisand degree of the alignment become weaker with Ec. The product molecular also hastendency to align along x+z and the tendency become weaker with Ecand j′tends toward anisotropic distribution as a function ofθt. It is indicating from P (θr)that j′is distributed withcylindrical symmetry in the product scattering frame and the direction of j′is preferentiallyperpendicular to k direction. The trend increase obviously with Ec, which is also confirmed bythe product rotational alignment factor. j′of product H'Br is oriented along the negativedirection of y-axis. And the orientation become more obvious with Ecin the energy rangconsidered in this investigation. Moreover the product also has a preference for left-handedproduct rotation in planes parallel to the scattering plane (k-k').In the sixth chapter, we produce potential energy curves (PECs) for the groundΧ¹ÃŽÂ£⁺andexcitedÎ’¹ÃŽÂ states of KH molecule. AlthoughΧ¹ÃŽÂ£⁺of KH has been extensively studied bothin experiment and theory, to the best of our knowledge, the analytical potential energyfunctions of this system from the ab initio energies have not been reported yet. Unlike theintense interest in the ground states,Î’¹ÃŽÂ state has received relatively little attention. Lee et alobserved theÎ’¹ÃŽÂ excited state for the first time and obtained some ro-vibrational levels,spectroscopic constants which could be used as reference standard for theoretical calculation.The theoretical results in the literature obviously deviate from the new experimental values,implying that there is still space to perform high level calculations for the state. Therefore, wecalculated the PECs for the two states mentioned above using MRCI and large basis set. Toinvestigate the correlation effect of core-valence electrons, we employ five schemes includingdifferent correlated electrons and different active spaces. We perform three correlationschemes for K. The first one includes core electrons 3s²3^p6. The second one includes coreelectrons 3^p6and the last one includes only the valence 4s¹. Two different (including 3dorbitals or not) sets of active spaces. The PECs are then fitted into Murrel–Sorbie functions.The spectroscopic parameters, ro-vibrational levels and transition frequencies are determinedbased on the APEFs, and compared with the experimental and theoretical data available atpresent. It is found that the present molecular properties forÎ’¹ÃŽÂ , which are better than those available in the literature, can be reproduced with calculations with the suitable correlatedelectrons and active space of orbitals.