Motivation
Ab initio Valence Bond (VB) theory(1) based on nonorthogonal orbitals has long been restricted to small systems because of the algebraic complexity and high computational costs associated with the use of nonorthogonal orbitals. The communities of developers and of users have thus both been very limited. On the other hand, VB theory has undeniable predictive power, which is enhanced by the direct connection it provides to chemists’ language and concepts, such as Lewis structures, resonance, and arrow-pushing notation. VB theory, therefore, is not merely merely useful for quantifying chemical phenomena, but provides a framework for advanced chemical concepts that continues to lead to new insights into electronic structure and chemical reactivity.(2)
Two scientific conferences coupled with tutorial on the XMVB program(3) have been organized in 20126 and 2015,7 the former being supported by CECAM as a « CECAM tutorial ». These events attracted a large number of chemists who were interested in applications of VB theory and who wanted to learn how to perform VB computations for themselves, confirming to us the widespread interest of computational chemists in such approaches. Furthermore, very recent breakthrough advances in nonorthogonal-based formalism have been made8 that, combined with modern implementation techniques (automatic formula and code generators), enabled a sharp increase in computational efficiency. Nonetheless, ab initio nonorthogonal VB programs(3-5) are still not as efficient as corresponding orthogonal orbital-based quantum chemistry software.
In parallel, and independently, the last few years have heralded a considerable upsurge of interest from outside the traditional VB community on nonorthogonal based electronic structure methods, including also approaches that are fairly closely related to VB theory.(9-12) Many of these strategies aim to provide physically correct and compact truncations of the exact wave function, and they are very promising for the future development of new black-box methods that are able to provide proper treatments of strongly-correlated systems and/or of excited states with much more compact wave functions.(13) (and thus at a reduced cost) relative to standard high-level ab initio electronic structure methods, such as orthogonal orbital-based CASPT2/MRCI, Coupled-Cluster, or Quantum Monte Carlo approaches.
[1] (a) Valence Bond Theory ; Cooper, D. L., Ed.; Elsevier: Amsterdam, The Netherlands, 2002. (b) Valence Bond methods - theory and applications ; Gallup G. A., Cambridge University Press, 2005. (c) Shaik, S.; Hiberty, P. C. A Chemist's Guide to Valence Bond Theory ; Wiley-Interscience: New York, 2008. (d) Su, P.; Wu, W., Ab Initio Non-orthogonal Valence Bond Methods, WIREs Compt Mol Sci., 2013, 3, 56. [2] Wu W., Su P., Shaik S. S. and Hiberty P. C., Chem. Rev., 2011, 111, 7557. [3] (a) Song, L.; Mo, Y.; Zhang, Q.; Wu, W. J. Comput. Chem. 2005, 26, 514. (b) http://www.xmvb.org [4] Verbeek J., Lagenberg J. H., Byrman C. P. and van Lenthe J. H., TURTLE and Ab Inito VB/VBSCF Program (1988-2000) [5] (a) Spin Coupled VB theory: Gerratt J., Cooper D. L., Karadakov P. B. and Raimondi M., Chem. Soc. Rev. 1997, 26, 87. (b) CASVB: Cooper D. L., Thorsteinsson T. and Gerratt J., Adv. Quantum Chem. 1999, 32, 51. [6] (a) Braïda B., Derat E., Humbel S., Hiberty P. C., and Shaik S. S., ChemPhysChem 2012, 13, 4029 (b) https://wiki.lct.jussieu.fr/workshop/index.php/VB_workshop_in_Paris [7] « The Chemical bond at the XIth Century », and Valence Bond tutorial in Xiamen: http://www.cb2015.org [8] (a) Chen, Z.; Chen, X.; Wu, W. J. Chem. Phys., 2013, 138, 164119 (b) Chen, Z.; Chen, X.; Wu, W. J. Chem. Phys., 2013, 138, 164120 (c) Chen, Z.; Chen, X.; Wu, W. J. Chem. Phys., 2014, 141, 134118 (d) Chen, X.; Chen, Z.; Wu, W., J. Chem. Phys., 2014, 141, 194113. [9] Nonorthogonal CI methods, see for instance: (a) Malmqvist P. Å., Int. J. Quantum Chem., 1986, 30, 479. (b) Thom A. J. W. and Head-Gordon M., J. Chem. Phys., 2009, 131, 124113. [10] For recent work on Geminal-based methods, see for instance: (a) Pawel T. ; Boguslawski, K. ; Ayers P. W PCCP, 2015, 17, 14427 (b) Jeszenszki, P ; Rassolov, V ; Surjan, PR ; Szabados, A 2015, 113, 249 (c) Small, DW ; Sundstrom, EJ ; Head-Gordon, M ; J. Chem. Phys., 2015, 142, 094112. [11] Quantum Monte Carlo with VB type of wave functions, see for instance: (a) Braïda, B.; Toulouse, J.; Caffarel, M.; Umrigar, C. J. J. Chem. Phys. 2011, 134, 084108−084118. (b) F. Fracchia, C. Filippi, C. Amovilli J. Chem. Theory Comput. 8, 1943 (2012). [12] Projected Hartree-Fock methods, see for instance: (a) Scuseria G. E., Jimenez-Hoyos C. A., Henderson T. M., Samanta K., and Ellis J. K., J. Chem. Phys., 2011, 135, 124108 (b) Jiménez-Hoyos A., Henderson T. M., Tsuchimochi T., and Scuseria G. E., J. Chem. Phys., 2012, 136, 164109 (c) Ellis J., Martin R., Scuseria G., J. Chem. Theory Comput., 2013, 9, 2857. [13] (a) Sundstrom E. J., Head-Gordon M. J. Chem. Phys., 2014, 140, 114103 (b) Wu, W.; Zhang, H.; Braïda, B.; Shaik, S. Theor. Chem. Acc., 2014, 133, 1441.