Content of the VB lectures

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The 8 Valence Bond lectures will provide a large overview of Valence Bond theory for chemistry, from qualitative to modern VB methods including their scope :

1. P. C. HIBERTY : «Qualitative Valence Bond theory» :
   Roots of VB theory - The two-electron bond - Polyatomic molecules – hybridization – Writing and representing VB wave functions - Bridges between Molecular Orbital (MO) and VB theories - VB formalism using an effective Hamiltonian and applications to some basic electronic structure problems.
2. P. C. HIBERTY : « An Overview of Ab initio Valence Bond methods» :
   Selecting a set of VB structures - General panorama of the two families of VB methods : methods based on localized orbitals, methods based on semi-delocalized orbitals - the Generalized Valence Bond (GVB) method - the Breathing-Orbital Valence Bond (BOVB) method - Calculating diabatic states - Current capabilities of the XMVB program.
3. W. WU : «Post-VBSCF methods including dynamical correlation» :
   Post-VBSCF methods include VBCI, VBPT2, DFVB, and VBSCF(CAS), and VB methods for solvation effect include VBPCM, VBEFP, combined QM(VB)/MM, etc.
4. P. SU : «Practical guide for VB calculations» :
   Practical indications on present capabilities of VB methods : which quantities can be computed with VB, which cpu cost for different methods/systems. Presentation of the XMVB program, structure of input/output. Running an XMVB calculation from scratch : basic examples.
5. D. L. COOPER : «Spin-Coupled VB, CASVB methods and applications» :
   Key principles underlying the CASVB algorithms are described, along with the basic formalism of spin-coupled VB. Various examples are presented, including recent multiconfigurational SC calculations. SLIDES
6. S. SHAIK : «Valence Bond diagrams for chemical reactivity /1» :
   The Valence Bond State Correlation Diagram (VBSCD) model : its general outlook on reactivity - construction of VBSCD for elementary processes - barrier expression based on VBSCD - making qualitative predictions with VBSCD.
7. S. SHAIK : «Valence Bond diagrams for chemical reactivity /2» :
   The Valence Bond Configuration Mixing Diagrams (VBCMD) : construction and application to chemical reactivity - VBCMD with intermediates nascent from «foreign states» - VBCMD for electronic delocalization in Clusters - Application of VBCMD to photochemical reactivity.
8. Y. MO : «Block-localized wavefunction (BLW) method and its applications» :
   The block-localized wavefunction (BLW) method is the simplest and most efficient variant of the ab initio valence bond (VB) theory. Extensive applications of this method to molecular structures, inter- and intra-molecular electron transfer and chemical reactivity will be presented and discussed.

The 5 extension lectures will provide connections with other modern wave function approaches for treating strong and dynamical electronic correlation, as well as with other insightful interpretative methods :

• C. LANDIS : «Density, NBOs, and Lewis-like Structures from Across the Periodic Table» :
  The NBO program performs Mathematical operations on the density matrix that provide various localized basis sets (natural atomic orbitals, natural bond orbitals, etc.) and their occupancies. This talk will focus on the application of NBO methods to a variety of bonding situations with an emphasis on revealing the underlying Lewis structures of molecules from across the periodic table.
• F. M. BICKELHAUPT : «MO Theory: Ally or Competitor of VB Theory?» :
  In my lecture, I will present the basic approach and techniques of modern, quantitative MO theory in combination with bond energy decomposition analyses. In particular, I will point out the ability of MO theory to integrate quantitative description with a causal and predictive physical model using the topics of aromaticity and hypervalence as concrete illustrations. Eventually, this leads me to address the title question: are MO and VB theories allies or competitors ?.
• G. SCUSERIA : Projected HF and beyond: Is there a VB connection? :
  I will present our recent results on symmetry-projected wave functions^1,2. For the Hartree-Fock case and spin projection, this is a 50-year old problem in quantum chemistry going back to Löwdin and his “extended HF” theory. For Hartree-Fock-Bogoliubov and number projection, our approach offers new perspectives on Antisymmetrized Geminal Power (AGP) wavefunctions that were the focus of much attention in the 1980s. In our work, all molecular symmetries (electron number, spin S^2 and S_z , point group, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. The resulting method yields a comprehensive black-box treatment of static correlation with one-electron (mean-field) computational cost. The ensuing wave function is of high quality multireference character competitive with CASSCF. The method can also be applied to calculate excited states and spectral functions³. I will discuss applications to the Hubbard model and frustrated Heisenberg model (spin liquid). The curse of the thermodynamic limit (the method is not size consistent) and the quest for a low-cost treatment of residual correlations will also be addressed. More importantly, I am eager to discuss and learn about the connections of our projection methods with VB genealogy, particularly when we include several non-orthogonal determinants in our ansatz as we do in Ref.³
  1. Projected quasiparticle theory for molecular electronic structure, G. E. Scuseria, C. A. Jimenez-Hoyos, T. M. Henderson, J. K. Ellis, and K. Samanta, J. Chem. Phys. 135, 124108 (2011).
  2. Projected Hartree-Fock theory, C. A. Jimenez-Hoyos, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 136, 164109 (2012).
  3. Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model, R. Rodrıguez-Guzman, K. W. Schmid, C. A. Jimenez-Hoyos, and G. E. Scuseria, Phys. Rev. B (2012) arXiv:1204.2006
• K. BOGUSLAWSKI : «Modern Multi-Determinantal Total-State Wave Functions and their Relation to One-Electron Pictures like Valence Bond Theory» :
  to be filled.
• J-P. MALRIEU : «VB reading of CASSCF and post CASSCF wave functions. The work of dynamical correlation» :
  Understanding the physical content of the electronic correlation requires a VB reading of the correlated wave functions. This reading proceeds through a definition of atom-centered or bond orbitals through a unitary transformation of the active MOs of CASSCF functions. It makes clear not only the physical mechanisms governing the non-dynamical correlation but also the qualitative effects of the dynamical correlation on both the energy and the valence wave function. The correspondance between the MO-CI and VB approaches will be systematically identified.