Analytic Potential Energy Functions And Molecular Constants Of Several Molecules And Total Cross Sections Of Electron Scattering By Molecules

Molecular potential energy function (PEF) is one of the importantfields in atomic and molecular physics. It gives one absolutedescription of molecular properties with Born-Oppenheimerapproximation. Namely, it can completely determine molecular energy,equilibrium geometry, force constants and spectroscopic parameters.At the same time, it is also the PEF of the core movement, which is thefoundation to investigate atomic and molecular collision and reactionand is of special importance in the atom-cluster growth, dissociationand stability analyses.The adiabatic excitation energies from the ground to eight excitedstates, A¹âˆ‘_u⁺, G¹âˆ_g, 2¹âˆ_u, a³âˆ‘_u⁺, b³âˆ_u, c³âˆ‘_g⁺, 2³âˆ‘_g⁺ and 2³âˆ_u, for dimer⁷Li₂ have been calculated using the SAC/SAC-CI method presented inGaussian03 program package. The reasonable dissociation limits ofthese excited states have been deduced according to the principles ofAtomic and Molecular Reaction Statics (AMRS) using the adiabaticexcitation energies obtained in this paper. The single-point energyscanning (SPES) calculations over a wide internuclear separationrange are performed using SAC method for the ground state andSAC-CI method for the eight excited states of dimer ⁷Li₂ at a numberof basis sets. All the ab initio calculations are fitted into analyticalPEFs by the least-squares method. Then, these analytical PEFs areemployed to calculate the spectroscopic parameters (D_e, R_e,ω_e,ω_ex_e,B_e andα_e) and some molecular constants (vibrational levels, classicalturning points, inertial rotation and centrifugal distortion constants).The calculated results are encouraging when compared with the measurements and other theories. Some of the calculated results arereported for the first time. In addition,(1) The present SAC/SAC-CI method cannot accurately performthe harmonic frequency calculations. The frequency is computed usingthe corresponding analytical PEF according to the Rydberg-Klein-Reesmethod. Comparison shows that most of them are in good agreementwith the experimental findings.(2) It has been found that the equilibrium internuclear separation R_eobtained by geometry optimization is different from the one obtainedby SPES calculations. The reason is that the unique GSUM methodused in the SPES calculations is incompletely identical with the oneused in the geometry optimization. It is the reason that the R_e resultobtained by SPES calculations is quite integrated into the PEF, and allthe spectroscopic data including R_e can be derived from the PEF, thusthe result obtained by SPES calculations should be more reasonable.The reasonable dissociation limits for the ground states of fivediatomics (Li₂, H₂, LiH, BH, AlH) and three triatomics (Li₂H, BH₂,AlH₂) have been determined employing the principles of ARMS. Theground-state equilibrium geometries of five diatomics are optimizedand their harmonic frequencies and dissociation energies are calculatedby the density-functional theory, coupled-cluster theory and quadraticconfiguration-interaction method including single and doublesubstitutions (QCISD). By comparison with the experiments, the mostsuitable methods and basis sets for further calculations are selected.Employing the selected methods and basis sets, the SPES calculationsare performed over a wide internuclear separation range. Theanalytical PEFs are obtained by the least-squares fitting using theSPES results, and then the spectroscopic parameters (ω_ex_e, B_e andα_e)are computed, which are in good agreement with the measurementswherever available.The geometry optimization is carried out using B3P86/D95V(d,p)method for the Li₂H ground state, QCISD/6-311++G(3df,3pd) method for the BH₂ ground state and QCISD/D95(3df,3pd) method for theAlH₂ ground state. The calculated results agree well with experimentalfindings. The conclusions are gained that their ground states are X²A₁.The analytical PEFs of Li₂H(C_2v, X²A₁), BH₂(C_2v, X²A₁) and AlH₂(C_2v,X²A₁)have been derived from the many-body expansion theory. Theanalytical PEFs describe correctly their configurations and dissociationenergies.Electron scattering from molecules is an important physical process.The total cross sections (TCSs) for electron-molecule scattering haveimportant applications in space, plasmas, laser, atmospheric scienceand chemistry physics. However, electron-molecule scattering presentsa more complex problem than corresponding electron-atom scatteringdue to the multi-center nature, the lack of a center of symmetry and itsnuclear motion. In addition, over the intermediate- and high-energyrange, almost all inelastic channels (rotational, vibrational, andelectronic excitation and ionization processes, etc) are opened, whichmakes the conventional theoretical calculations for electron-moleculescattering becomes almost impossible to carry out.The electron-molecule scattering problem is reduced to the electron-atom scattering one by the additivity rule (AR) model which is easierto handle. The AR model assumes that an atom in a molecule is a freeone, thus the interactions between them can be neglected. In fact,bonded atoms in a molecule are not identical with the ones in free statedue to the overlapping effect of electron clouds. The overlapping effectmakes electron clouds of a bonded atom distorted and thus itsspherical symmetry destroyed. Having taking into consideration theoverlapping effect of electron clouds between two bonded atoms in amolecule, a modified complex optical potential is presented. The TCSsof electron scattering by HCl, NH₃, H₂O, CH₄, N₂, O₂ and CO₂ arecalculated using the modified potential and the AR model at Hartree-Fock level at 30 to 5000 eV and compared with those obtained byexperiments and other theories, and good agreement is obtained over a wide energy range. Careful examinations show that the present resultsare still larger than the measurements at low-energy range but smallerthan those at high-energy range. It suggests that further modificationsof complex optical potential must be related with the energy ofincident electrons.A close-packed polyatomic molecule is not fully transparent forlow-energy electrons, and the "inner" atoms are partially shielded bythe "outer" atoms and do fewer contributions to the molecular TCS atlower energies than those at higher energies. Taking into considerationthe changes of the geometric shielding effect in a molecule as theincident electron energy varies, an empirical fraction, which exhibitsthe TCS contributions of shielded atoms in a molecule at differentenergies, is presented. In order to clarify that the problem, of whichTCS for electron-molecule scattering varies much fast as energy ofincident electrons, is caused by TCS calculation accuracy of electron-atom scattering or by AR model in itself, we use the experimental TCSresults of electron scattering by C, H, O and N to calculate the TCS ofelectron scattering from NO, N₂O, NO₂, CO₂, H₂O, CH₄, C₂H₂, C₂H₄and C₂H₆ by the modified AR model at 50-5000 eV. By comparisonwith experimental findings, we have found that the TCSs calculated bythe modified AR model are in excellent agreement with almost all theexperiments over the whole overlapping energy range. Whereas theTCSs obtained by the original AR model gradually become in goodaccord with the measurements only when energy is above 200-300 eVor more for more complex molecules, and the problem, of which TCSfor electron-molecule scattering varies much fast as energy of incidentelectrons, still exists. Thus the conclusion can be gained that theproblem is caused by AR model itself. The conclusion is very usefulwhere the complex optical potential needs further modifications.