Springer Series on Atomic, Optical, and Plasma Physics 105 Larry A. Viehland Gaseous Ion Mobility, Diffusion, and Reaction Springer Series on Atomic, Optical, and Plasma Physics Volume 105 Editor-in-chief GordonW.F.Drake,DepartmentofPhysics,UniversityofWindsor,Windsor,ON, Canada Series editors JamesBabb,Harvard-SmithsonianCenterforAstrophysics,Cambridge,MA,USA Andre D. Bandrauk, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, QC, Canada Klaus Bartschat, Department of Physics and Astronomy, Drake University, Des Moines, IA, USA Philip George Burke, School of Mathematics and Physics, Queen’s University, Belfast, UK Robert N. Compton, Knoxville, TN, USA Tom Gallagher, University of Virginia, Charlottesville, VA, USA Charles J. Joachain, Faculty of Science, Université Libre Bruxelles, Bruxelles, Belgium Michael Keidar, School of Engineering and Applied Science, George Washington University, Washington, DC, USA Peter Lambropoulos, FORTH, IESL, University of Crete, Iraklion, Crete, Greece Gerd Leuchs, Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Erlangen, Germany PierreMeystre, OpticalSciences Center, Universityof Arizona, Tucson, AZ,USA The Springer Series on Atomic, Optical, and Plasma Physics covers in a comprehensive manner theory and experiment in the entire field of atoms and molecules and their interaction with electromagnetic radiation. Books in the series provide a rich source of new ideas and techniques with wide applications in fields such as chemistry, materials science, astrophysics, surface science, plasma technology, advanced optics, aeronomy, and engineering. Laser physics is a particular connecting theme that has provided much of the continuing impetus for new developments in the field, such as quantum computation and Bose-Einstein condensation. The purpose of the series is to cover the gap between standard undergraduate textbooks and the research literature with emphasis on the fundamental ideas, methods, techniques, and results in the field. More information about this series at http://www.springer.com/series/411 Larry A. Viehland Gaseous Ion Mobility, Diffusion, and Reaction 123 Larry A.Viehland Science Department ChathamUniversity Pittsburgh, PA,USA ISSN 1615-5653 ISSN 2197-6791 (electronic) SpringerSeries onAtomic, Optical, andPlasma Physics ISBN978-3-030-04493-0 ISBN978-3-030-04494-7 (eBook) https://doi.org/10.1007/978-3-030-04494-7 LibraryofCongressControlNumber:2018962124 ©SpringerNatureSwitzerlandAG2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Acknowledgements ItisapleasuretoacknowledgethemajorcontributionsofRainerJohnsen(Chaps.1,2, and 7), William F. Siems (Chap. 3), Timothy G. Wright (Chap. 6), Alexei A. Buchachenko (Chap. 6), and Claudia K. Viehland (figures and photos). Contributionsthatareofsmallerextentbutperhapsequalsignificanceweremadeby Douglas E. Goeringer and Robert E. Robson. This book is devoted to all of these peopleandtothememoryofIsadoreAmdur,CharlesF.Curtiss,EdwardA.Mason, andEarlW.McDaniel. v Notation and Abbreviations aðr;tÞ Acceleration vector as a function of r and t, Sect. 4.1 arð2;sTÞ 2T Matrix elements of Jj for one gas in a mixture, Sect. 5.6 aðMTÞð(cid:2)(cid:2)(cid:2)Þ MT Matrix elements of J for one gas in a mixture, Sect. 5.7 j j a Atomic unit of distance, the bohr, Sect. 6.3 0 A Vector potential in Maxwell’s equations, Sect. 6.16 A Vector representation of area, Sect. 1.9 A00 Constant used to extract Xð1;1Þ from mobility data, Sect. 2.8.4 aug-cc.. cc.. basis set augmented to include diffuse functions, Sect. 6.11.1 b Impact parameter of a collision, Sect. 1.11 b Ions in a pulse entering the drift tube, Sect. 2.4 1 brð2;sTÞ 2T Matrix elements of Jj for one gas or a mixture, Sect. 5.6 bðMTÞð...Þ MT Matrix elements of J for one gas or a mixture, Sect. 5.7 j B Magnetic field strength, Sect. 2.11 B Magnetic field vector, Sect. 1.15 Bðkm;pqstÞ Basis functions of a 2T treatment of molecules, Sect. 8.7 BMM Beyond Monchick–Mason approximation, Sect. 8.10 BSSE Basis set superposition error, Sect. 6.11.3 c Speed of light in a vacuum, Sect. 6.16 c Constant term in various equations cl;m;r Expansion coefficient for fðr;v;tÞ, Sect. 5.4 c ;c Correction terms in Eq. (1.9), Sect. 1.8 2 4 C Coefficient of r(cid:3)3 in long-range potential, Sect. 8.11 3 C Coefficient of r(cid:3)4 in long-range potential, Sect. 6.22 4 Cb4 Value of C4 in atomic units, Sect. 6.22 C6 Coefficient of r(cid:3)6 in long-range potential, Sect. 9.1 C Coefficient of r(cid:3)n in short-range potential, Sect. 9.1.3 n cc.. Family of correlation consistent basis functions, Sect. 6.11.1 cc-p cc basis set with polarized orbitals vii viii NotationandAbbreviations cc-pC.. cc basis set with polarized core orbitals, Sect. 6.11.1 cc-pwC.. ccbasissetwithpolarized,weightedcoreorbitals,Sect.6.11.1 CAS Complete active space, Sect. 6.13 CASSCF Complete active space SCF method, Sect. 6.13 CBS Complete basis set, Sect. 6.11.1 CC Coupled-cluster method, Sect. 6.12.1 CI Configuration interaction, Sect. 6.12.1 CP Counterpoise correction, Sect. 6.11.3 d Rigid sphere diameter, Sect. 1.11 d Dimensionless ratio in f ðgÞ, Sect. 7.2 L rel d Dimensionless ratio in f ðgÞ, Sect. 7.2 T rel D Ion diffusion coefficient (a scalar), Sect. 1.9 D Ion diffusion tensor, Sect. 1.9 D Ion diffusion coefficient along E or B, Sect. 1.9 L D Hall component of D, Sect. 1.15 H D Ion diffusion coefficient perpendicular to E, Sect. 1.9 T D Same as D , Sect. 6.23 x T D Same as D , Sect. 6.23 z L Dk Same as DL, Sect. 1.15 D? Same as DT, Sect. 1.15 d-aug-cc.. cc.. basis set doubly augmented with diffuse functions, Sect. 6.11.1 D Doubles in a CI calculation, Sect. 6.10 DMS Differential IMS, Sect. 2.8.4 DTMS Drift-tube mass spectrometer, Sect. 2.2 e Fundamental charge, Sect. 2.8.2 E Electric field strength, Sect. 1.1 E Average excess energy in a ping-pong experiment, Sect. 2.9.1 E~ Time-independent total energy, Sect. 6.3 E Electric field vector, Sect. 1.8 E Atomic unit of energy, the hartree, Sect. 6.3 h E Ion kinetic energy in swarm frame, Sect. 4.5 ion E Ion kinetic energy in laboratory frame, Sect. 4.5 k E Energy of nth state in perturbation theory, Sect. 6.18 n E Electrical potential energy, Sect. 1.3 p E Total energy, Sect. 6.3 tot Eð0Þ Energyforasimplerprobleminperturbationtheory,Sect.6.18 EbEb Energy dyadic in laboratory frame, Sect. 4.5 E=n Reduced field strength, Sect. 1.1 0 ECP Effective core potential, Sect. 6.4.6 f Ion distribution function of many variables, Sect. 8.1 f Fraction of collisions that cool an ion, Sect. 3.5.2 c f Fraction of collisions that heat an ion, Sect. 3.5.2 h fðvÞ Ion speed distribution function, Sect. 1.8 NotationandAbbreviations ix fðvÞ Ion velocity distribution function, Sect. 5.1 fðr;v;tÞ Ion distribution as a function of r, v and t, Sect. 4.1 fð2TÞðkm;:Þ Expansion coefficient for f of molecular ions, Sect. 8.7 f ðvÞ Zero-order ion velocity distribution function, Sect. 5.4 0 fð1TÞðvÞ Zero-order ion vdf in 1T theory, Sect. 5.5 0 fð2TÞðvÞ Zero-order ion vdf in 2T theory, Sect. 5.6 0 fðMTÞðvÞ Zero-order ion vdf in MT theory, Sect. 5.7 0 f ðvÞ Gram–Charlier ion vdf, Sect. 7.2 GC fðvÞ Velocity distribution function of neutral j, Sect. 5.2 j j f ðv Þ Velocity distribution function of reactive neutral R, Sect. 7.1 R R fðr;v;tÞ Distribution as a function of r, v and t of neutral j, Sect. 4.2 j j j f ðgÞ Relative vdffor an ion–reactive neutral pair, Sect. 7.2 rel fRðbRÞðvRÞ Vdf of reactive R in state bR as a function of vR, Sect. 3.4.3 f ðr;v ;tÞ DistributionofreactiveRasafunctionofr,v andt,Sect.4.3 R R R F Electrical force, Sect. 1.3 F Functional operator, Sect. 5.2 Fðr;tÞ External force as a function of r and t, Sect. 4.1 Fk Full width at half height, Sect. 2.4 FAIMS Field-asymmetric ion mobility spectrometer, Sect. 2.9 g Relative speed before collision, Sect. 3.2 g0 Relative speed after collision, Sect. 3.3 g Relative velocity before collision, Sect. 3.3 g0 Relative velocity after collision, Sect. 3.4 G Center-of-mass velocity before collision, Sect. 3.3 G0 Center-of-mass velocity after collision, Sect. 3.3 GC Gram–Charlier, Sect. 5.9 GER Generalized Einstein Relation, Sect. 1.19 h Planck’s constant, Sect. 6.3 H Hamiltonian operator, Sect. 6.3 H0 Difference operator in perturbation theory, Sect. 6.18 Hð0Þ H for a simpler problem in perturbation theory, Sect. 6.18 H Internal Hamiltonian for molecules, Sect. 8.1 int H ðxÞ Hermite polynomial of order p for variable x, Sect. 5.7 p HF Hartree–Fock method, Sect. 6.8 HPCCS High Performance Collision Cross Section, Sect. 9.7 pffiffiffiffiffiffiffi i Base of the imaginary numbers, (cid:3)1, Sect. 6.3 I Electric current (in Ch. 1 only), Sect. 1.4 I Moment of inertia of a molecular ion, Sect. 8.7 I Moment of inertia of a molecule of type j, Sect. 8.5 j ICR Ion cyclotron resonance, Sect. 2.12 IMS Ion mobility spectrometer, Sect. 2.7 IMS/MS IMS with a mass spectrometer 2.8 IMoS Computer program for mobility simulation, Sect. 9.7 x NotationandAbbreviations IOS Infinite-order sudden approximation, Sect. 8.10 ITSIM Computer program for ion trap simulation, Sect. 2.13 j Ion (or current density) flux vector, Sect. 1.9 j Index labeling non-reactive gases, Sect. 1.8 J Pre-collision ion angular momentum vector, Sect. 8.5 J0 Post-collision ion angular momentum vector, Sect. 8.5 J Pre-collision angular momentum vector of j, Sect. 8.5 j J0 Post-collision ion angular momentum vector, Sect. 8.5 j J Angular momentum of a pure neutral gas, Sect. 8.8 0 J Pre-collision angular momentum vector of R, Sect. 8.5 R J Boltzmann collision operator for neutral j, Sect. 4.2 j J Collision operator for reactive neutral R, Sect. 4.3 R k Reaction rate coefficient, Sect. 1.9 ek Parameter in VðrÞ, Sect. 6.15.3 kðr;tÞ Reaction rate coefficient as a function of r and t, Sect. 4.8 k Boltzmann’s constant, Sect. 1.9 B K Ion mobility (a scalar), Sect. 1.8 K Ion mobility (a tensor), Sect. 1.15 K0 Logarithmic derivative of K, Sect. 1.19 K Hall component of K, Sect. 1.15 H K Ion mobility along a magnetic field, Sect. 1.15 L K Standard ion mobility (a scalar), Sect. 1.8 0 K0;n Nominal value of K0, Sect. 2.2.5 K Ion mobility perpendicular to magnetic field, Sect. 1.15 T KE Kinetic energy in the center-of-mass frame, Sect. 7.3 cm L Length of apparatus, Sect. 1.1 L Relative angular momentum, Sect. 8.8 0 Lðlþ1=2Þ Associated Laguerre polynomial, Sect. 5.5 r LCAO Linear combination of atomic orbitals, Sect. 6.7 LDA Local density approximation, Sect. 6.2 m Ion mass, Sect. 1.7 mb Ion mass fraction, Sect. 2.7.1 m Mass of neutral j in a mixture, Sect. 5.2 j m Neutral mass, Sect. 2.6.1 0 m Mass of neutral isotope 1, Sect. 2.6.1 1 m Mass of neutral isotope 2, Sect. 2.6.1 2 m Mass of reactive neutral R, Sect. 5.2 R mb Neutral mass fraction, Sect. 2.7.1 0 M Molar mass of ion, Sect. 1.13 M Molar mass of reactive neutral gas R, Sect. 1.17 R M Molar mass of neutral gas molecules, Sect. 1.1 0 M Weighted average of neutral masses, Sect. 2.6.3 MBPT Many-body perturbation theory, Sect. 6.12.1