Low-energy electron scattering by CF 4 , CCl 4 , SiCl 4 , SiBr 4 , and SiI 4 Ma ´ rcio T. do N. Varella, Alexandra P. P. Natalense,* Ma ´ rcio H. F. Bettega, and Marco A. P. Lima Instituto de Fı ´sica ‘‘Gleb Wataghin,’’ Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, Sa ˜ o Paulo, Brazil and Departamento de Fı ´sica, Universidade Federal do Parana ´, Caixa Postal 19081, 81531-990 Curitiba, Parana ´, Brazil ~Received 1 September 1998; revised manuscript received 12 July 1999! In this paper, we show elastic and rotationally inelastic cross-section calculations of low-energy electron scattering by CF 4 , CCl 4 , SiCl 4 , SiBr 4 , and SiI 4 . The fixed-nuclei static-exchange scattering amplitudes were obtained with the Schwinger multichannel method with soft norm-conserving pseudopotentials. We show elastic integral and differential cross sections and discuss the role of the basis set on the nature of some structures seen in a previous publication @A. P. P. Natalense et al., Phys. Rev. A 52, R1 ~1995!#. We have attributed these structures to linear dependency in the basis set caused by the symmetric combination ( x 2 1y 2 1z 2 )exp(2ar 2 ). The rotational cross sections were calculated with the help of the adiabatic-nuclei- rotation approximation. Our results are in good agreement with available experimental data. The sums of 0 →0,3,4,6 rotational cross sections in general show good agreement with the elastic ~rotationally unresolved! ones. The rotationally summed integral cross section agrees within 0.3% with the elastic integral cross section for CF 4 at 7.5 eV, and within 26% for SiI 4 at 30 eV. It was found that rotationally inelastic cross sections are considerably large for such molecules, because the heavy peripheral atoms play a significant role as scattering centers. @S1050-2947~99!00611-3# PACS number~s!: 34.80.Bm, 34.80.Gs I. INTRODUCTION Recently, studies on collisions of low-energy electrons with molecules have experienced great improvement, espe- cially for molecules such as CH 4 , SiH 4 , CCl 2 F 2 , CF 4 , CCl 4 , etc. @1#. The resulting cross sections play an important role in the modeling of cold plasmas. In these plasmas ‘‘hot’’ electrons collide with ‘‘cold’’ molecules generating ions, at- oms, and radicals which are responsible for industrially in- teresting processes ~etching, polimerization, nitriding, etc.!. However, calculation of scattering cross sections for large molecules by ab initio methods quickly reaches computa- tional limitations. The ab initio methods in current use that are able to deal with molecules with arbitrary geometries are the Schwinger multichannel ~SMC! method @2#, the complex Kohn varia- tional method @3#, and the polyatomic version of the R-matrix method @4#. In this paper, we discuss in detail the results obtained using the Schwinger multichannel method in conjuction with norm-conserving pseudopotentials ~SMCPP! @5#. This combined method allows studies on molecules with hundreds of electrons. The basic idea involved in this proce- dure is to replace the core electrons and the nucleus of each atom in the molecule by the corresponding soft norm- conserving pseudopotential and to describe the valence elec- trons in a many-body framework ~Hartree-Fock approxima- tion in the present implementation!. The resulting atomic wave functions are nodeless and smooth and can be ex- panded in smaller basis sets. Furthermore, these norm- conserving pseudopotentials were designed to work in differ- ent environments ~atoms, molecules, solids!@6# and we have shown that the SMCPP can provide very good results in many different situations as bound-state calculations @5# and scattering calculations in different approximations ~elastic @5,7,8#, electronic excitations by electron impact @9,10#, and rotational excitation cross sections @11,12#!. This is a full length paper, which includes the results of a previous Rapid Communication @7# together with new results for differential, partial, and rotational excitation cross sec- tions for CF 4 , CCl 4 , SiCl 4 , SiBr 4 , and SiI 4 . Here we are dealing with the static-exchange approximation, which we regard as an initial step towards more elaborate calculations including electronic excitations and polarization effects. These fixed-nuclei elastic scattering amplitudes, however, can be readily used to obtain rotational excitation cross sec- tions through the adiabatic-nuclei-rotation ~ANR! approxi- mation. This approach, combining scattering amplitudes ob- tained with the help of pseudopotentials and the ANR approximation, has been successfully applied to moderately large molecules (CH 4 , SiH 4 , GeH 4 , PbH 4 @11# and NH 3 , PH 3 , AsH 3 , SbH 3 @12#! and we are now extending its appli- cation to larger systems. As pointed out by Jung et al. @13#, pure rotational energy transfer from electrons to molecular gases is often quite ef- fective. Even though the energy transfer per collision is quite small for polyatomic molecules, the cross sections are very large, 10 216 cm 2 or even more. In spite of their importance for these cold plasmas, we were not able to find rotationally resolved cross sections reported for the molecules studied in this paper. Theoretical works are mainly restricted by the computational limitations referred to above, whereas experi- mentalists run up against insufficient resolution of experi- mental devices. Mu ¨ ller et al. @14# have reported experimental rotationally resolved cross sections for methane. Those mea- surements took advantage of a broadening, caused by pure rotational excitations, of energy-loss peaks. However, since *Present address: Department of Chemistry, Texas A& M Univer- sity, College Station, TX 77843-3255. PHYSICAL REVIEW A NOVEMBER 1999 VOLUME 60, NUMBER 5 PRA 60 1050-2947/99/60~5!/3684~10!/$15.00 3684 ©1999 The American Physical Society