Fundamental World Of Quantum Chemistry

by Brandas, Erkki; Kryachko, Eugene S.; Lowdin, Per-Olov

• ISBN13: 9781402025839
• ISBN10: 1402025831
• Format: Hardcover
• Copyright: 2005-07-30
• Publisher: Kluwer Academic Pub

Summary

Per-Olov Löwdin's stature has been a symbol of the world of quantum theory during the past five decades, through his basic contributions to the development of the conceptual framework of Quantum Chemistry and introduction of the fundamental concepts; through a staggering number of regular summer schools, winter institutes, innumerable lectures at Uppsala, Gainesville and elsewhere, and Sanibel Symposia; by founding the International Journal of Quantum Chemistry and Advances in Quantum Chemistry; and through his vision of the possible and his optimism for the future, which has inspired generations of physicists, chemists, mathematicians, and biologists to devote their lives to molecular electronic theory and dynamics, solid state, and quantum biology.Fundamental World of Quantum Chemistry: Volumes I, II and III form a collection of papers dedicated to the memory of Per-Olov Löwdin. These volumes are of interest to a broad audience of quantum, theoretical, physical, biological, and computational chemists; atomic, molecular, and condensed matter physicists; biophysicists; mathematicians working in many-body theory; and historians and philosophers of natural science. The volumes will be accessible to all levels, from students, PhD students, and postdocs to their supervisors.

Table of Contents

G.G. Hall
Per-Olov Löwdin	1	(2)
Stockholm-Uppsala Symposium	1	(1)
Visiting Uppsala 1957-58	1	(1)
Assessment	2	(1)
J.-M. André
In Silico Chemistry: Past, Present and Future	3	(20)
Introduction	3	(4)
In Silico Chemistry, Past and Present	7	(3)
In Silico Chemistry, Future	10	(6)
Conclusions	16	(3)
Acknowledgements	19	(1)
Notes	20	(1)
References	20	(3)
J. Katriel
Weights of Spin and Permutational Symmetry Adapted States for Arbitrary Elementary Spins	23	(20)
1. Introduction	23	(2)
2. Methodology of the Present Exploration	25	(5)
2.1. Generating the data	25	(4)
2.2. Analysis of the data	29	(1)
3. One and Two Particle States	30	(1)
4. Three Particle States	30	(2)
5. Four Particle States	32	(1)
6. Five Particle States	33	(3)
7. Some Six-Particle States	36	(1)
8. Attempt at a Generalization	37	(4)
8.1. Modularity strings	37	(1)
8.1.1. Repetition of modularity strings	37	(1)
8.1.2. Composition of modularity strings	38	(1)
8.1.3. Absorption of a modularity string	38	(1)
8.1.4. Amalgamation of modularity strings	38	(1)
8.1.5. Irreducible modularity string	38	(1)
8.2. Towards a generalizing conjecture	38	(3)
9. Conclusions	41	(1)
Acknowledgements	41	(1)
References	41	(2)
B.L. Burrows and M. Cohen
Schrödinger's Wave Equation - A Lie Algebra Treatment	43	(24)
1. Introduction	44	(2)
2. Some One-Dimensional Problems	46	(8)
2.1. The Heisenberg algebra	46	(4)
2.2. The SO(3) and SO(2,1) algebras	50	(4)
3. Problems in Two Space Variables	54	(7)
3.1. Single term perturbations	57	(1)
3.2. Two-term perturbations	57	(2)
3.3. Three-term perturbations	59	(1)
3.4. Four-term perturbations	60	(1)
Appendix A: Complex Extensions of Some Real Lie Algebras	61	(1)
Appendix B: The Algebra 0(5) and Some of Its Subalgebras	62	(3)
Acknowledgements	65	(1)
References	65	(2)
M.R. Kibler and M. Daoud
On Supersymmetric Quantum Mechanics	67	(30)
1. Introducing Supersymmetry	67	(4)
2. A Generalized Weyl-Heisenberg Algebra Wk	71	(6)
2.1. The algebra Wk	71	(1)
2.2. Projection operators for Wk	72	(1)
2.3. Representation of Wk	72	(1)
2.4. A deformed-boson + k-fermion realization of Wk	73	(2)
2.4.1. The realization of Wk	73	(2)
2.4.2. Actions on the space F	75	(1)
2.5. Particular cases for Wk	75	(2)
3. A General Supersymmetric Hamiltonian	77	(6)
3.1. Axiomatic of supersymmetry	77	(1)
3.2. Supercharges	77	(2)
3.3. The general Hamiltonian	79	(1)
3.4. Particular cases for the Hamiltonian	80	(1)
3.5. A connection between fractional sQM and ordinary sQM	81	(2)
4. A Fractional Supersymmetric Oscillator	83	(3)
4.1. A special case of Wk	83	(1)
4.2. The resulting fractional supersymmetric oscillator	83	(1)
4.3. Examples	84	(16)
4.3.1. Example 1	84	(1)
4.3.2. Example 2	85	(1)
5. Differential Realizations	86	(2)
6. Closing Remarks	88	(1)
Acknowledgments	89	(1)
Appendix A: Connection Between Wk and Uy(sl)	89	(1)
Appendix B: A Q-uon • Boson + k-Fermion Decomposition	90	(3)
References	93	(4)
P.W. Langhoff, J.A. Boatz, R.J. Hinde, and J.A. Sheehy
Application Of Löwdin's Metric Matrix: Atomic Spectral Methods for Electronic Structure Calculations	97	(18)
1. Introduction	98	(1)
2. Definition of the Atomic Spectral-Product Basis	99	(1)
3. Hamiltonian Matrix in the Spectral-Product Basis	99	(1)
4. Convergence in the Spectral-Product Basis	100	(8)
4.1. Prior Antisymmetry	100	(2)
4.2. Metrically-Defined Hamiltonian Representation	102	(1)
4.3. Removal of Linear Deepnndece in the Moffitt Basis	103	(2)
4.4. Isolation of the Antisymmetric Spectral-Product Subspace	105	(2)
4.5. Equivalence of Prior and Post Antisymmetry	107	(1)
5. Illustrative Calculations -The Electron Pair Bond	108	(5)
6. Concluding Remarks	113	(1)
Acknowledgments	113	(1)
References	113	(2)
F.E. Harris
Integrals for Exponentially Correlated Four-Body Systems of General Angular Symmetry	115	(14)
Dedication	115	(1)
1. Introduction	116	(1)
2. Wavefunctions	117	(2)
3. Matrix Elements	119	(1)
4. Angular Integration	119	(3)
5. Rotational Invariants	122	(2)
6. Radial Integration	124	(1)
7. Discussion	125	(1)
Acknowledgments	126	(1)
Appendix: Angular Momentum Identities	126	(1)
References	127	(2)
P.R. Suján and Á. Szabados
Appendix to "Studies in Perturbation Theory": The Problem of Partitioning	129	(1)
1. Introduction	130	(1)
2. The Concept of Partitioning	131	(2)
3. Traditional Partitionings in Quantum Chemistry	133	(54)
3.1. Epstein-Nesbet partitioning	133	(3)
3.2. Adams partitioning	136	(1)
3.3. Mødler-Plesset partitioning	136	(2)
4. Level Shifts	138	(1)
4.1. Basic definition	138	(1)
4.2. Connection between MP and EN	139	(1)
4.3. Complex level shifts	139	(1)
5. Feenberg Scaling	140	(1)
6. Optimized Partitioning	140	(1)
6.1. General formulation	141	(1)
6.2. Properties of the optimized partitioning	142	(4)
6.2.1. Vanishing of the third order correction	142	(1)
6.2.2. Consequence on the higher orders	142	(1)
6.2.3. Extensivity	143	(1)
6.2.4. Resummation of RS-PT series	143	(2)
6.2.5. Derivation by projection operator technique	145	(1)
6.3. The example of the anharmonic oscillator	146	(1)
7. Optimized Partitioning in Single Reference PT	146	(3)
8. Using Noncanonical Orbital Energies in MBPT	149	(1)
8.1. Davidson-Kapuy partitioning	149	(2)
8.2. Dyson partitioning	151	(1)
8.3. Optimized orbital energies in MBPT	152	(3)
Optimized orbitals in MBPT: Lindgren's approach	154	(1)
9. Zero order Hamiltonians with Two-Body Terms	154	(1)
10. Optimized Partitioning with Multi-Configurational Zero Order	155	(5)
10.1. Multi-configurational perturbation theory	155	(3)
10.1.1. Generalized MP partitioning	156	(1)
10.1.2. Generalized DK partitioning	157	(1)
10.1.3. Generalized Dyson partitioning	157	(1)
10.1.4. Generalized EN partitioning	158	(1)
10.2. Optimized partitioning in multi-reference theories	158	(2)
10.2.1. Optimized partitioning in MCPT	158	(1)
10.2.2. Witek-Nakano-Hirao approach	158	(1)
10.2.3. Freed's optimization approach	159	(1)
11. Minimizing the Norm of RW	160	(5)
11.1. On the convergence of the PT series	160	(1)
11.2. The norm of RW	161	(2)
11.3. Properties of the RW-optimized partitioning	163	(2)
11.3.1. Uniqueness	163	(1)
11.3.2. Uncoupled nature	164	(1)
11.3.3. Degeneracy elimination	165	(1)
12. Constant Denominator PT	165	(3)
12.1. Unsøld approximation	165	(1)
12.2. Optimized Unsøld approximation: CMX2	166	(2)
13. Perturbation Corrections to Ionization Energies	168	(5)
13.1. The ionization operators subspace	169	(1)
13.2. PT formulae for single ionization	170	(2)
13.3. Optimal level shifts for the ionization potential	172	(1)
Acknowledgments	173	(1)
References	174	(13)
I. Mayer and A. Hamza
Treating Nonadditivity as a Perturbation: a Quasi-Particle Formalism	187	(12)
Introduction	187	(1)
1. The Quasi-Additive Hamiltonian	188	(7)
1.1. Preliminary remarks	188	(3)
1.2. The quasi-particle Hamiltonian	191	(1)
1.3. Nonadditivity as a perturbation	192	(2)
1.4. Example	194	(1)
2. Transformation of the Hamiltonian	195	(2)
3. Summary	197	(1)
4. Dedication	197	(1)
Acknowledgments	198	(1)
References	198	(1)
P. Lazzeretti
Unified Approach to Intensities in Vibrational Spectroscopies via Dynamic Electromagnetic Shieldings at the Nuclei of a Molecule	199	(16)
1. Introduction	199	(2)
2. The Expectation Value of the Electric Field at the Nuclei of a Molecule	201	(3)
3. Hellmann-Feynman Geometrical Derivative of the Dynamic Polarisability	204	(4)
4. Hellmann-Feynman Geometrical Derivative of the Optical Rotatory Power	208	(3)
5. Concluding Remarks	211	(1)
Acknowledgments	212	(1)
References	212	(3)
I. Lindgren
Comparison Between the Many-Body Perturbative and Green's-Function Approaches for Calculating Electron Binding Energies and Affinities: Brueckner and Dyson Orbitals	215	(32)
1. Introduction	215	(1)
2. Many-Body Perturbation Theory	216	(9)
2.1. The Bloch equation	216	(2)
2.2. Second quantization and the particle-hole formalism	218	(4)
2.3. Graphical representation of MBPT	222	(1)
2.4. Linked-diagram expansion	223	(2)
3. MBPT Treatment of a Single Electron Outside Closed Shells	225	(10)
3.1. The pair approximation	226	(1)
3.2. The removal energy	227	(3)
3.3. Brueckner and Dyson orbitals	230	(4)
3.4. Application to the alkali atoms	234	(1)
4. The Propagator or Green's-Function Method	235	(6)
4.1. Definition of the Green's function	235	(1)
4.2. The Fourier transform of the Green's function	236	(1)
4.3. The perturbation expansion	237	(2)
4.4. The Dyson equation	239	(1)
4.5. Application to the affinity of the calcium atom	240	(1)
5. Summary and Conclusion	241	(1)
Acknowledgments	242	(1)
References	243	(4)
S. Larsson
Quantum Chemistry, Localization, Superconductivity, and Mott-Hubbard U	247	(10)
1. Introduction	247	(2)
2. Pairing	249	(1)
3. Mott-Hubbard U Cannot Predict Localization	250	(1)
4. Two-Electron Transfer Is Possible Only If CDW Interacts with SDW State	251	(1)
5. What Can Be Explained?	252	(2)
6. Conclusion	254	(1)
References	254	(3)
I.B. Bersuker
Reformulation of the Concept of Jahn-Teller Vibronic Coupling Effects in Theoretical Chemistry	257	(16)
1. Introduction	257	(1)
2. Earlier and More Recent Formulations	258	(3)
3. Extensions Based on the PJTE and Interatomic (Intermolecular) Interactions	261	(5)
4. Illustration to Some of the Latest Achievements	266	(3)
5. Conclusions	269	(1)
References	269	(4)
R. Krems and A. Dalgarno
Collisions of Atoms and Molecules in External Magnetic Fields	273	(22)
1. Introduction	273	(2)
2. Close Coupling Theory of Collisions in a Magnetic Field	275	(3)
3. Collisions of P-, D- and F-State Atoms with Structureless Targets	278	(4)
4. Collisions of ³Σ-Molecules and ²S-Atoms Without Hyperfine Interaction	282	(4)
5. Collisions of ³Σ-Molecules and ²S-Atoms with Hyperfine Interaction	286	(1)
6. Transport Cross Sections	287	(3)
7. Summary	290	(2)
References	292	(3)
A.T. Amos, B.L. Burrows, and S.G. Davison
Effects of Orbital Overlap on Calculations of Charge Exchange in Atom-Surface Scattering	295	(28)
1. Introduction	296	(1)
2. Preliminaries	297	(6)
2.1. Fundamental equations with overlap	297	(3)
2.2. Partitioning technique	300	(1)
2.3. Matrix elements for SIN	301	(2)
3. The Two-State Model of SIN	303	(11)
3.1. Use of a non-orthogonal set	303	(2)
3.2. Orthogonal orbitals	305	(1)
3.3. Approximate solutions	306	(1)
3.4. Example calculations	307	(7)
4. The Many-State Model of SAI	314	(5)
4.1. Matrix elements	314	(1)
4.2. Narrow-band approximation	314	(2)
4.3. Wide-band approximation	316	(3)
5. Conclusions	319	(1)
Acknowledgements	320	(1)
References	320	(3)
G.L. Malli
Relativistic Quantum Chemistry of Heavy and Superheavy Elements: Fully Relativistic Coupled-Cluster Calculations for Molecules of Heavy and Transactinide Superheavy Elements	323	(1)
1. Introduction	324	(2)
2. Challenges in Experimental and Theoretical Transactinide Chemistry	326	(1)
3. Relativistic Effects in Compounds of Actinide and Superheavy Elements	326	(2)
4. Dirac-Fock-Breit SCF Formalism of Malli and Oreg for Molecules of Heaviest Elements	328	(2)
5. Relativistic Coupled-Cluster Methodology	330	(3)
6. Universal Gaussian Basis Set for Dirac-Fock-Breit and Relativistic Coupled-Cluster Calculations for Molecules of Heavy and Superheavy Elements	333	(1)
7. Dirac-Fock-Breit Calculations for Molecules of the Transactinide Superheavy Elements	334	(1)
8. Results and Discussion of Our All-Electron Dirac-Fock-Breit Calculations	334	(31)
8.1. Tetrachlorides of Rf, Hf, Zr and pentachlorides of Db, Ta and Nb	334	(3)
8.2. All-electron fully relativistic Dirack-Fock calculations for SgBr6 and SgBr6±	337	(1)
8.3. Nonrelativistic Hartree-Fock SCF calculations for SgBr6 and SgBr6±	337	(2)
9. Relativistic Effects in Bonding and Binding for SgBr6 and SgBr6±	339	(2)
10. Hexachloride and Hexafluoride of the Superheavy Element Seaborgium	341	(1)
11. Oxychlorides of Seaborgium, Nielsbohrium and Tungsten	342	(2)
12. Tetroxides of Superheavy Hassium and Its Lighter Congener Osmium	344	(1)
13. Dramatic Antibinding Effects due to Relativity in Compounds of Superheavy Elements Ekaplatinum (E110), Ekagold (E111) and Ekamercury (E112)	345	(3)
13.1. Our relativistic DF SCF calculations predict E112F2 and 112C12 to be bound	347	(1)
13.2. Our relativistic DF SCF calculations predict 112F4 and HgF4 to be unbound	348	(1)
14. Relativistic and Electron Correlation Effects for Molecules of Heavy Elements: Fully Relativistic Coupled-Cluster Calculations for PbH4	348	(4)
15. Relativistic Dirack-Fock SCF Calculations for Molecules of Transactinide Superheavy Elements: RfC14	352	(3)
15.1. Nonrelativistic Hartree-Fock SCF calculations for the superheavy RfCl4	352	(2)
15.2. Dirack-Fock-Breit SCF calculations for the superheavy RfCl4	354	(1)
16. Ab initio Fully Relativistic Coupled-Cluster Singles and Doubles (RCCSD) Calculations for Molecules of Superheavy Transactinide Elements: Rutherfordium Tetrachloride RfCl4	355	(4)
Conclusions	359	(1)
Acknowledgments	359	(2)
References	361	(4)
U. Kaldor, E. Eliav, and A. Landau
Study of Heavy Elements by Relativistic Fock Space and Intermediate Hamiltonian Coupled Cluster Methods	365	(42)
1. Introduction	365	(1)
2. Basic Formulation	366	(3)
2.1. The relativistic Hamiltonian	366	(1)
2.2. The one-electron equation	367	(2)
3. Electron Correlation: the Fock-Space Coupled Cluster Method	369	(3)
4. The Intermediate Hamiltonian Method	372	(12)
4.1. Formulation	372	(3)
4.2. Selection of Pm and Pi model spaces	375	(1)
4.3. Atomic excitation energies not accessible by Fock-space CC	376	(3)
4.3.1. Excitation energies of Ba	376	(1)
4.3.2. Excitation energies of xenon and radon	376	(3)
4.4. New formulation	379	(1)
4.5. Mixed-sector intermediate Hamiltonian approach	380	(2)
4.6. Pilot applications of the mixed-sector intermediate Hamiltonian method	382	(2)
4.6.1. Group 14 electron affinities	382	(1)
4.6.2. Group 15 ionization potentials	383	(1)
4.6.3. Silver, gold and eka-gold	384	(1)
5. Applications: Heavy Elements	384	(5)
5.1. When is an atom "heavy"? Ionization potentials of alkali atoms	385	(2)
5.2. Gold atom: local maximum of relativistic effects	387	(1)
5.3. Electron affinities of alkali atoms - accuracy at the 5 meV level	388	(1)
6. Application: Superheavy Elements	389	(11)
6.1. Ground state of rutherfordium - relativity vs. correlation	390	(1)
6.2. Ground state configuration of eka-gold (element 111)	391	(2)
6.3. Eka-Hg (E112) and eka-Tl (E113) - what chemistry?	393	(1)
6.4. Eka-lead (element 114) - an island of stability?	394	(4)
6.5. Electron affinity of the rare gas El 18 - how important is QED?	398	(1)
6.6. Eka-actinium (E121) - when is the Breit term important?	399	(1)
7. Summary and conclusion	400	(1)
References	401	(6)
I. Goidenko and L. Labzowsky
QED Effects in Heavy Elements	407	(16)
Introduction	407	(2)
1. Evaluation of the Lamb shift	409	(8)
Electron self-energy in frames of the potential expansion	409	(5)
Vacuum polarization	414	(3)
2. Radiative Corrections for the ns Electrons in Heavy and Superheavy Atoms	417	(2)
3. Conclusion	419	(1)
Acknowledgements	420	(1)
References	420	(3)
M. Quack
Time and Time Reversal Symmetry in Quantum Chemical Kinetics	423	(52)
Why After All? Scientists at Work	424	(2)
1. What Are Time, Time Reversal Symmetry and Irreversibility?	426	(3)
2. Reversible Atomic and Molecular Dynamics, Atomic and Molecular Clocks	429	(5)
3. De Facto (Apparently) Irreversible Molecular Dynamics	434	(11)
3.1. Irreversibility and entropy in chemical reactions leading to equilibrium	434	(2)
3.2. Quantum dynamics of functional groups from high resolution spectroscopy and the phenomenon of intramolecular vibrational redistribution by quantum delocalization	436	(7)
3.3. Entropy and irreversibility in the quantum dynamics of highly excited, single, isolated molecules	443	(2)
4. Fundamental Symmetries, Conservation Laws, Non-Observable Quantities, and Symmetry Violations in Physics	445	(3)
5. Molecular Chirality and de lege Parity Violation (Space Reflection Symmetry)	448	(2)
6. Time Reversal Symmetry, Stereochemistry, CPT Symmetry and an Absolute Molecular Clock	450	(2)
7. Molecular Irreversibility and a Possible Molecular Quantum Psychology	452	(12)
7.1. Thought formation as a molecular, irreversible decision	452	(3)
7.2. Physical chemical boundary conditions of free will	455	(7)
7.3. The image of mankind: people, society, ants and anthills	462	(2)
8. Per-Olov Lowdin as a Teacher: A Personal Recollection by Martin Quack from the Summer School 1973 and a Later Event (1996)	464	(7)
Acknowledgement	471	(1)
References	471	(4)
F.J. Luque, A. Bidon-Chanal, J. Muñoz-Muriedas, I. Soteras, C. Curutchet, A. Morreale, and M. Orozco
Solute-Solvent Ineractions from QM SCRF Methods Analysis of Group Contributions to Solvation	475	(22)
1. Introduction	475	(2)
2. Methods	477	(7)
2.1. The MST Continuum Model	477	(1)
2.2. Perturbative Treatment of the electrostatic free energy	478	(2)
2.3. Charge normalization	480	(2)
2.4. Partitioning of the solvation free energy	482	(2)
3. Empirical versus MST Hydration Group Contribution	484	(5)
4. Application of Fractional Models in Drug Design	489	(3)
5. Conclusions	492	(1)
Acknowledgments	493	(1)
References	493	(4)
A.V. Tulub
The Cavity Model with a Surface Formed by Two Intersecting Spheres. An Analytical Treatment	497	(24)
1. Introduction	497	(3)
2. Laplace's Equation in Toroidal Coordinates and Its Solution	500	(4)
3. Integral Equations for Functions Am(τ) and Bm(τ)	504	(4)
4. Charge Densities and Total Charges Induced on Surfaces	508	(3)
5. Interpretation of Formulas in Terms of the Method of Images	511	(4)
6. Internal Dirichlet Problem	515	(3)
Acknowledgments	518	(1)
Personal Impressions	518	(1)
References	519	(2)
S. Bubin, M. Cafiero, and L. Adamowicz
Quantum Mechanical Calculations on Molecules Containing Positrons	521	(26)
1. Introduction	522	(7)
2. Outlook	529	(2)
3. The Method	531	(6)
3.1. Hamiltonian	532	(1)
3.2. Basis set	533	(2)
3.3. Symmetry	535	(1)
3.4. Variational calculations	536	(1)
3.5. Parallel implementation	537	(1)
4. e+LiH	537	(2)
5. Summary and Future Work	539	(1)
Acknowledgments	539	(1)
Dedication	539	(1)
References	540	(7)
S. Mahalakshmi and D.L. Yeager
Low-Lying Ionization Potentials of B3N and Photodetachment Energies of B3N- Using The Multiconfigurational Spin Tensor Electron Propagator Method	547	(16)
1. Introduction	547	(2)
2. Theory	549	(2)
3. Results and Discussion	551	(8)
3.1. Ionization potentials of B3N	551	(4)
3.1.1. B3N linear	552	(1)
3.1.2. B3N rhombic	553	(2)
3.2. Photodetachment energies of B3N-	555	(48)
3.2.1. B3N- linear	555	(2)
3.2.2. B3N- rhombic	557	(2)
4. Summary and Conclusions	559	(1)
5. Acknowledgements	559	(1)
6. References	560	(3)
M.L. Coote, A. Pross, and L. Radom
Understanding Alkyl Substituent Effects in R-O Bond Dissociation Reactions in Open- and Closed-Shell Systems	563	(18)
1. Introduction	564	(1)
2. Theoretical Procedures	565	(1)
3. Poor Performance of B3-LYP for R-O Bond Energies	566	(5)
4. Trends in R-X Bond Dissociation Energies in Closed-Shell Systems	571	(4)
5. Trends in R-O β-Scission in Open-Shell Systems	575	(3)
6. Conclusions	578	(1)
7. References	578	(3)
S. Canuto, K. Coutinho, and B.J. Costa Cabral
Hydrogen Bonding and The Energetics of Homolytic Dissociation in Solution	581	(20)
1. Introduction	582	(2)
2. Microsolvation	584	(2)
3. Monte Carlo Simulations	586	(5)
4. Hydrogen Bonding and Homolytic Dissociation: Sequential Monte Carlo/Quantum Mechanics Calculations	591	(4)
5. Summary and Conclusions	595	(1)
6. Dedication	596	(1)
Acknowledgements	596	(1)
References	596	(5)
C.M. Jansson, P.-E. Larsson, N. Salhi-Benachenhou, G. Bergson, and S. Lunell
Theoretical Calculations of Kinetic Isotope Effects for a Series of Substituted Aziridines	601	(18)
1. Introduction	602	(1)
2. Calculations of Kinetic Isotope Effects	603	(6)
2.1. Transition state theory	604	(2)
2.2. Variational transition state theory	606	(2)
2.3. Tunneling corrections	608	(1)
3. Aziridine Isotope Effects	609	(5)
4. Computational Details	614	(1)
Acknowledgements	615	(1)
References	615	(4)
C.A. Tsipis, A.C. Tsipis, and C.E. Kefalidis
Exploring The Catalytic Cycle of the Hydrosylilation of Alkenes Catalyzed by Hydrido-Bridged Diplatinum Complexes Using Electronic Structure Calculation Methods	619	(26)
1. Introduction	619	(2)
2. Computational Details	621	(1)
3. Results and Discussion	622	(19)
3.1. Equilibrium geometries, electronic, spectroscopic and bonding properties of the model "precatalysts"	622	(6)
3.2. Equilibrium geometries, electronic, spectroscopic and bonding properties of the model "catalysts"	628	(1)
3.3. The catalytic cycle of the hydrosilylation of ethene using the model "catalysts" I, II and III	629	(17)
3.3.1. Hydrosilylation of ethene with H3SiH using model catalyst I. A representative model catalytic cycle	629	(4)
3.3.2. Hydrosilylation of ethene with C13SiH using model catalyst II. The role of the hydrosilane on the catalytic activity	633	(2)
3.3.3. Hydrosilylation of ethene with H,SiH using model catalyst III. The role of the "spectator" phosphane ligand on the catalytic activity	635	(2)
3.3.4. Hydrosilylation of vinyl chloride with H3SiH using model catalyst I. The role of the olefin on the catalytic activity and regioselectivity	637	(4)
4. Epilogue	641	(1)
References	642	(3)
W.H.E. Schwarz
Towards A Physical Explanation of The Periodic Table (PT) of Chemical Elements	645	(26)
1. Historical and Conceptual Basis of the Periodic Table (PT)	646	(7)
1.1. Classifying the Materials: Chemical Elements	646	(1)
1.2. Chemical Atomism and Valence: Numbers	646	(2)
1.3. Families or Groups of Elements: Similarity	648	(1)
1.4. Two-Dimensional Arrangement: The Periodic 'Law'	648	(1)
1.5. Bohr's Model of the Hydrogen Atom: One-Electron States	649	(1)
1.6. Atoms with Few Valence Electrons: Alkali Metals	650	(1)
1.7. Madelung's Rule and the PT: Contradictions	650	(1)
1.8. Lowdin: Three Relevant Remarks	651	(1)
1.9. Conclusions: The Pertinent Questions	652	(1)
2. Some Pertinent Problems Solved Long Ago or Just Recently	653	(2)
2.1. Chemical Similarity of Elements	654	(1)
2.2. Periodicity of Properties	654	(1)
3. Atomic Orbitals and Atomic Shells	655	(8)
3.1. Preliminary remarks on orbitals	655	(1)
3.2. Atomic ground state and ground configuration	656	(1)
3.3. Orbital energies and total energies	657	(1)
3.4. Horizontal trends	658	(3)
3.5. Hartree-Fock or Kohn-Sham, restricted and unrestricted	661	(1)
3.6. Common AO level ordering	662	(1)
3.7. Atomic orbitals in chemical compounds	662	(1)
4. Concluding Remarks	663	(1)
Acknowledgments	664	(1)
References	664	(7)
Index	671