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Theoretical Methods That Help Understanding the Structure and Reactivity of Gas Phase Ions International Journal of Mass Spectrometry 240 (2005) 37–99 Review Theoretical methods that help understanding the structure and reactivity of gas phase ions J.M. Merceroa, J.M. Matxaina, X. Lopeza, D.M. Yorkb, A. Largoc, L.A. Erikssond,e, J.M. Ugaldea,∗ a Kimika Fakultatea, Euskal Herriko Unibertsitatea, P.K. 1072, 20080 Donostia, Euskadi, Spain b Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, MN 55455-0431, USA c Departamento de Qu´ımica-F´ısica, Universidad de Valladolid, Prado de la Magdalena, 47005 Valladolid, Spain d Department of Cell and Molecular Biology, Box 596, Uppsala University, 751 24 Uppsala, Sweden e Department of Natural Sciences, Orebro¨ University, 701 82 Orebro,¨ Sweden Received 27 May 2004; accepted 14 September 2004 Available online 25 November 2004 Abstract The methods of the quantum electronic structure theory are reviewed and their implementation for the gas phase chemistry emphasized. Ab initio molecular orbital theory, density functional theory, quantum Monte Carlo theory and the methods to calculate the rate of complex chemical reactions in the gas phase are considered. Relativistic effects, other than the spin–orbit coupling effects, have not been considered. Rather than write down the main equations without further comments on how they were obtained, we provide the reader with essentials of the background on which the theory has been developed and the equations derived. We committed ourselves to place equations in their own proper perspective, so that the reader can appreciate more profoundly the subtleties of the theory underlying the equations themselves. Finally, a number of examples that illustrate the application of the theory are presented and discussed. © 2004 Elsevier B.V. All rights reserved. Keywords: Ab initio molecular orbital electronic structure theory; Density functional theory; Time dependent density functional theory; Quantum Monte Carlo theory; Surface hopping; Two-state reactivity Contents 1. Introduction .......................................................................................................... 38 2. Molecular orbital theory ............................................................................................... 39 2.1. The Hartree–Fock approximation ................................................................................. 41 2.2. The symmetry breaking problem ................................................................................. 42 2.3. The electron correlation ......................................................................................... 43 2.4. (Multi)configuration interaction .................................................................................. 44 2.4.1. Full CI ................................................................................................ 46 2.4.2. Truncated CI methods ................................................................................... 46 2.5. Coupled cluster theory .......................................................................................... 47 2.6. Many body perturbation theory (MBPT) .......................................................................... 48 2.7. Quantum Monte Carlo........................................................................................... 50 ∗ Corresponding author. Tel.: +34 430 18190; fax: +34 943 212236. E-mail address: [email protected] (J.M. Ugalde). 1387-3806/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ijms.2004.09.018 38 J.M. Mercero et al. / International Journal of Mass Spectrometry 240 (2005) 37–99 2.7.1. Trial wave functions .................................................................................... 50 2.7.2. Variational Monte Carlo ................................................................................. 51 2.7.3. Diffusion Monte Carlo .................................................................................. 51 2.7.4. Pseudopotentials........................................................................................ 53 3. Density functional methods ............................................................................................ 53 3.1. The Hohenberg–Kohn theorem ................................................................................... 55 3.1.1. The proof of the theorem ................................................................................ 56 3.1.2. The Levy formulation ................................................................................... 56 3.1.3. The energy variational principle .......................................................................... 56 3.2. The Kohn–Sham formulation .................................................................................... 58 3.3. Fractional occupation numbers ................................................................................... 59 3.4. The exchange-correlation functional .............................................................................. 61 3.4.1. The experimental route to the exchange-correlation hole .................................................... 62 3.4.2. The local (spin) density approximation .................................................................... 63 3.4.3. The failures of the local density approximation ............................................................ 64 3.4.4. The gradient expansions ................................................................................. 64 3.4.5. Generalarized gradient approximations.................................................................... 64 3.4.6. Meta generalized gradient approximations................................................................. 66 3.5. Hybrid functionals .............................................................................................. 66 3.6. Time dependent density functional theory ......................................................................... 67 3.6.1. Time-dependent density-functional response theory ........................................................ 67 3.6.2. Full solution of TDDFT Kohn–Sham equations ............................................................ 69 4. Surface-hopping and two-state reactivity ................................................................................ 70 4.1. Spin–orbit coupling ............................................................................................. 70 4.2. Transition probabilities .......................................................................................... 71 4.3. Transition metal compounds ..................................................................................... 72 4.4. Kinetic calculations ............................................................................................. 74 5. Illustrative examples .................................................................................................. 74 + 5.1. Getting chemical insight from the analysis of the Kohn–Sham orbitals: the aromaticity of B13 ......................... 74 5.2. Weak intermolecular interactions ................................................................................. 76 5.3. Dissociation energies of ferrocene ion–molecule complexes ......................................................... 79 5.4. Electron detachment energies .................................................................................... 80 + 5.5. Discordant results on the FeO +H2 reaction reconciled by quantum Monte Carlo theory .............................. 82 5.6. Stability and aromaticity of Bi Ni rings and fullerenes .............................................................. 83 2+ 2+ 5.7. Electronic metastable bound states of Mn2 and Co2 ............................................................. 85 5.8. Charge induced fragmentation of biomolecules .................................................................... 87 + 5.9. Photodissociation of He3 ....................................................................................... 89 5.10. Optical properties of GFP ...................................................................................... 90 5.11. Surface hopping and reactivity: the overall reaction rate coefficient ................................................. 91 Acknowledgments ......................................................................................................... 94 References................................................................................................................ 94 1. Introduction disk drives, and affordable computer clusters with advanced Quantum chemistry and computer modeling nowadays visualization capabilities. Indeed, the availability of powerful has a major impact on the chemist’s ways of thinking and computers has succeeded in changing the face of theoretical working, as the role of both theoretical understanding and chemistry in general and quantum chemistry in particular computational modeling is becoming increasingly important [1]. In some areas, of which gas-phase ion chemistry is most in chemical research. prominent [2], quantum chemistry can provide results with Quantum chemistry has enjoyed the benefits of the re- an accuracy approaching that of the experiments and with a markable achievements in computer technology over the past freedom to consider rare or even “impossible” species and decades. Technological advances include increasingly more configurations which are hardly accessible for experimental powerful and lower-cost
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