Advances in Quantum Chemistry (eBook)

Thematic title: From Electronic Structure to Time-Dependent Processes

eBook Download: PDF

1999 | 1. Auflage
394 Seiten
Elsevier Science (Verlag)
978-0-08-058261-0 (ISBN)

Infos

Advances in Quantum Chemistry publishes articles and invited reviews by leading international researchers in quantum chemistry. Quantum chemistry deals particularly with the electronic structure of atoms, molecules, and crystalline matter and describes it in terms of electron wave patterns. It uses physical and chemical insight, sophisticated mathematics and high-speed computers to solve the wave equations and achieve its results. Advances highlights these important, interdisciplinary developments.

Inhalt

Front Cover 1
Advances in Quantum Chemistry, Volume 36 4
Copyright Page 5
Contents 6
Contributors 12
Preface 16
Biographic Notes 20
Chapter 1. Half a Century of Hybridization 24
1. Introduction: A Perennial Concept 25
2. Theoretical Determination Methods of Hybrid Orbitals 28
3. Conclusion: A Multiple-Purpose Instrument 40
References 44
Chapter 2. Core and Valence Electrons in Atom-by-Atom Descriptions of Molecules 50
1. Introduction 51
2. Working Formulas 53
3. Results 54
4. Conclusions and Prospects 62
Glossary 65
References 66
Chapter 3. From Classical Density Functionals to Adiabatic Connection Methods: The State of the Art 68
1. Introduction 69
2. Theoretical Background 70
3. Applications 82
4. Conclusion 94
References 95
Chapter 4. Exchange-Energy Density Functionals as Linear Combinations of Homogeneous Functionals of Density 100
1. Introduction 101
2. Theory: Exchange-Energy Density Functional 102
3. Computational Methods 105
4. Results and Discussion 106
5. Summary 113
References 113
Chapter 5. Density Functional Computations and Mass Spectrometric Measurements. Can This Coupling Enlarge the Knowledge of Gas-Phase Chemistry? 116
1. Introduction 117
2. Theoretical Background 117
3. Results and Discussion 123
4. Conclusions 139
References 139
Chapter 6. A Recent Development of the CS INDO Model: Treatment of Solvent Effects on Structures and Optical Properties of Organic Dyes 144
1. Introduction 145
2. Electrostatic Solvent Effects within the CS INDO Scheme 148
3. Results and Discussion 155
4. Conclusions 169
References 171
Chapter 7. Regioselectivity and Diastereoselectivity in the 1,3-Dipolar Cycloadditions of Nitrones with Acrylonitrile and Maleonitrile: The Origin of ENDO/EXO Selectivity 174
1. Introduction 174
2. Experimental Results 176
3. Computational Methods 177
4. Transition Structures and Activation Parameters 178
5. Solvent Effects 180
6. Comparison with the Experimental Results 181
7. Origin of Endo/Exo Selectivity: Analysis of TS structures 182
8. Origin of Endo/Exo Selectivity: Analysis of Activation Barriers 185
9. Conclusions 188
References 189
Chapter 8. Solvent-Mediated Proton Transfer Reactions in Cytosine: An Abinitio Study 192
1. Introduction 192
2. Theoretical Methods 193
3. Results and Discussion 194
4. Conclusions 204
References 204
Chapter 9. Electron Correlation at the Dawn of the 21st Century 208
1. Introduction 209
2. Electron Correlation in Very Small Atoms and Molecules 210
3. Many-Electron Methods in Terms of One-Electron Basis Sets 213
4. The Convergence with the Basis Size and the R12 Method 222
5. Localized Correlation Methods 225
6. Density Functional Methods 228
7. Conclusions 235
References 238
Chapter 10. Approximate Coupled Cluster Methods: Combined Reduced Multireference and Almost-Linear Coupled Cluster Methods with Singles and Doubles 254
1. Introduction 255
2. Externally Corrected CCSD 257
3. Almost-Linear (AL) CC Methods 259
4. Results and Discussion 262
5. Conclusions 269
References 272
Chapter 11. The Half Projected Hartree-Fock Model for Determining Singlet Excited States 276
1. Introduction 277
2. The HPHF Function for the Singlet Ground State 280
3. The HPHF Equations for Excited States 285
4. Applications 287
5. Discussions and Conclusions 291
References 292
Chapter 12. Complexation of Transition Metal Cations (Sc+, Fe+, Cu+) by One Cyanide Radical 294
1. Monocoordinated Complexes as Molecular Models and Chemical Species 295
2. Quantum-Mechanical Predictions 296
3. Final Remarks on the Complexation by the CN Ligand 303
References 304
Chapter 13. On the Photophysics of Molecules with Charge-Transfer Excitations between Aromatic Rings 306
1. Introduction 307
2. Biaryls and Related Molecules 308
3. A Simple Vibronic Model 311
4. The Time Evolution 317
5. Concluding Remarks 321
References 322
Chapter 14. Proton Assisted Electron Transfer 324
1. Introduction 324
2. Proton Assisted Electron Transfer 326
3. The Driving Force for PA-ET 329
4. Effect of a Peptide Bridge 330
5. Dynamical Features of the PA-ET Mechanism 335
6. Application to a Real System 338
7. Conclusions 342
8. Computational Details 342
Bibliography 343
Chapter 15. Lanczos Calculation of the X2A1/A2B2 Nonadiabatic Franck– Condon Absorption Spectrum of NO21 346
I . Introduction 347
2. Method 347
3. Results 351
4. Conclusions 361
References 363
Chapter 16. Hyperspherical Coordinates for Chemical Reaction Dynamics 364
1. Introduction 365
2. Separation of Radial and Angular Variables: Orbital Angular Momentum 366
3. Near Separability: Adiabatic and Diabatic Representations 367
4. Three-Body Problem: Orbital and Rotational Angular Momentum 370
5. Hyperspherical Coordinates and Harmonics: Hyperangular Momentum 373
6. Hyperspherical Mapping of Potential Energy Surfaces: Alternative Parametrization of Hyperangles 378
7. Perspectives and Concluding Remarks 382
References 383
Chapter 17. On the Einstein–Podolsky–Rosen Paradox 388
1. Introduction 389
2. The System Density Matrix 391
3. Reduced Density Matrices: Spin Correlation 393
4. An Example: Density Functions for the Hydrogen Molecule 396
5. Dissociation of the Hydrogen Molecule 398
6. The General Case 400
7. Conclusion 404
References 406
Index 408

Textauszug

Core and valence electrons in atom-by-atom descriptions of molecules

Sándor Fliszár1; Edouard C. Vauthier2; Vincenzo Barone3    1 Département de Chimie. Universiié de Montréal, CP 6128 Succ. Centre-ville, Montréal, Québec, H3C 3J7 Canada.
2 Institut de Topologie et de Dynamique des Systémes, 1, rue de la Brosse, Paris, France.
3 Dipartimento di Chimica, Università di Napoli ‘Federico II, via Mezzocannone 4. Napoli, Italia 1-80134

Abstract

The core-valence electron partitioning in molecules is adequately described by the energy formulas Ekv = (Vk − Vne,kc + Vkcv)/γkv for the valence region of atom k in a molecule and Ekion = (Vne,kc − Vkcv)/γkc for the kth ionic core left after removal of the valence electronic charge, where Vk and Vne,kc are, respectively, the total potential energy involving center k and the core nuclear-electronic potential energy of its Nkc core electrons. Vkcv denotes the interaction between Nkc and the electronic and nuclear charges found outside the core region k. Properly selected γkv and γkc parameters, treated as constants, lead to valence-region energies in good agreement with those deduced from the total molecular energies E and the equation Ev = E − ∑ kEkion. The point-charge-potential model for Vkcv, embodied in Vkcv = − Nkc[(Vk − Vne,kc)/Zk], improves the accuracy of the results. These formulas are best suited for atom-by-atom (or bond-by-bond) descriptions of molecules because Ekv is expressed solely in terms of the appropriate electrostatic potentials at the individual nuclei and does not depend on any particular mode of partitioning a molecule into atomic subunits.

1 Introduction

Two popular concepts of chemistry are tackled in this paper, namely i) the partitioning of the electronic charge of ground-state atoms, ions and molecules into core and valence parts and ii) the mental decomposition of molecules into ‘atomic subunits’. The familiar core–valence separation, of course, translates the old idea that chemical properties are largely governed by the outer (or valence) atomic regions, while the subdivision into ‘atomic’ subunits aknowledges the fact that atoms-in-the-molecule – such as those defined by Bader [1], for example – are convenient model building blocks for the interpretation of molecular properties. Both concepts are intuitively appealing but neither is cast in formal theory and the way they overlap certainly merits attention.

Let us first comment on the theoretical partitioning of a molecule into atomic subunits. The total energy. E, of that molecule in its ground state is most appropriately expressed as a sum of atomic-like terms Ek, with no extra contributions, i.e., E = ∑ kEk. (Incidentally, note that this atom-by-atom decomposition of a molecule easily transforms into an equivalent bond-by-bond description of the same [2,3]: the concept of a molecule viewed as a collection of chemical bonds is just another facet of the atoms-in-a-molecule description.) Now, little needs be added in that matter because – as we shall see – our results do not depend on the way the virtual boundaries of the atomic-like subunits in that molecule are defined. What does matter, however, is that such a partitioning is consistently made in real space.

Turning now to the core–valence separation of electronic charge, theory is relatively straightforward in the familiar orbital space where the energy is partitioned from the outset into orbital energies εi = ε1s, ε2s, etc. Things are somewhat more involved in real space, however, if we abandon the orbital-by-orbital electron partitioning in favor of a description based on the stationary ground-state electron density ρ(r) [3] − [6]. Sure, our real-space and the orbital-space core–valence separations appear for what they are: two facets of the same reality, but the real-space approach is clearly preferred in the present context because atom-by-atom (or bond-by-bond) descriptions are by their very nature treated in real space.

In real space, our core–valence separation is valid only for discrete solutions, namely for Nc = 2 core electrons for the first-row elements or Nc = 2 and 10 e for the second row. For ground-state atoms, ions and molecules we get [3]–[6]:

v=13Tv+2Vv

  (1)

kion=13Tkc+2Vne,kc+Vee,kcc

  (2)

=Ev+∑kEkion

  (3)

(1) for the valence-region energy Ev, (2) for the energy Ekion of the kth ionic core – i.e., the ion left behind after removal of the valence-region electrons – and (3) for the total energy, E, of the entire system, atom, ion or molecule. Equations (1)–(3) were successfully tested for atoms and ions, both near the Hartree–Fock limit [4] and with SDCI wave functions [5]. Numerous examples were also given for molecules [6], using SCF Gaussian-type basis sets.

Yet, these formulas are not congenial with our atom-by-atom descriptions. This is primarily due to a host of two-electron Coulomb and exchange terms – such as valence-other-valence and core-other-valence multi-center integrals – which, besides being intrinsically complex, require beforehand specification of the boundaries delimiting the individual ‘atoms’ in a molecule. Hence the idea of bypassing this sort of problem in favor of a considerably simplified approach, one that highlights the rôle of the electrostatic potentials.

The total (electronic and nuclear) potential energy involving nucleus Zk,

k=−Zk∫0∞ρrr−Rkdr+Zk∑l≠kZlRkl,

  (4)

plays a prominent part in the formulas developed earlier [3,4,6], such as

atomvk=1γkvVk−Vne,kc+Vkcv

  (5)

kion=1γkcVne,kc−Vkcv

  (6)

where and γkv are γkc valence and core parameters, respectively, of atom k. (These equations apply both to isolated atoms and to atoms in a molecule.) At first, it does not seem relevant to inquire into these γkv and γkc parameters. Indeed, if 1/γv denotes the appropriate average (in a molecule) of all the individual (1/γkv)’s weighted by the (Vk − Vne,kc + Vkcv) terms of Eq. (5), one can show that [3,6]

−γvEv=∑i∫valviϕi*F^ϕidτ

  (7)

where ∫ val … dτ means: integration over the valence space, ^ and ϕi being the familiar Hartree–Fock operator and the ith eigenfunction with occupancy vi. respectively. Combining this result with the formula Ev = ∑ kEatomvk using Eq. (5), one eliminates γv and gets Eq. (1). We proceed in a similar manner to get rid of the parameters and end up with Eq. (2). Briefly, the γkc parameters are not an issue in our final energy formulas (1)–(3). In the present instance, however, we find it useful to examine the γkv and γkc parameters and their merits in energy calculations featuring the total electrostatic potentials at the nuclei. In this perspective, remembering the definition of Vne,kc,

ne,kc=−Zk∫0rb,kρrr−Rkdr,

  (8)

we obtain...

Produkt-Details

• Erscheint lt. Verlag: 18.10.1999
• Mitarbeit: Herausgeber (Serie): Vincenzo Barone, Erkki J. Brandas, Alessandro Lami, John R. Sabin, Michael C. Zerner; Chef-Herausgeber: Per-olov Lowdin
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-10: 0-08-058261-3 / 0080582613
• ISBN-13: 978-0-08-058261-0 / 9780080582610