Assessing the performance of ab initio classical valence bond methods for hydrogen transfer reactions Itay Karach a , Alina Botvinik a , Donald G. Truhlar b , Wei Wu c , Avital Shurki a,⇑ a Institute for Drug Research, School of Pharmacy, The Hebrew University of Jerusalem, Jerusalem, 91120, Israel b Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455-0431, USA c The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China article info Article history: Received 7 May 2017 Received in revised form 22 May 2017 Accepted 23 May 2017 Available online xxxx Keywords: Valence bond Benchmark Hydrogen transfer reactions Strongly correlated systems abstract Ab initio classical valence bond theory in terms of localized orbitals has several advantages over elec- tronic structure methods based on canonical delocalized Hartree-Fock molecular orbitals, with two key distinctions being greater applicability to inherently multiconfigurational systems (also called multiref- erence systems or strongly correlated systems) and great interpretability in terms of covalent and ionic valence bond configurations (also called valence bond structures). This can be especially advantageous for applications to chemical reactions. However, until now only limited work tested the quantitative accuracy for the energetics of chemical reactions. The present study provides such tests and validations for a representative test set of six barrier heights corresponding to forward and reverse barriers of three hydrogen transfer reactions. In particular, we test the valence bond self-consistent-field theory (VBSCF) and three post-VBSCF methods that use VBSCF as a reference function for adding dynamic correlation, in particular valence bond configuration interaction (VBCI), breathing orbital valence bond (BOVB), and valence bond second-order perturbation theory (VBPT2). The VBSCF method itself is, as expected, not quantitatively accurate, with a mean unsigned error (MUE) for the six barrier heights of 17 kcal/mol. But the post-VBSCF methods are found to be quite successful. Depending on the basis set, and valence bond structure selection we obtain MUEs (in kcal/mol) as low as 3.7 for VBCI, 4.5 for BOVB, and (using a bigger basis-set) 1.3 for VBPT2. These compare well, on the same data set, with 1.6 for coupled clusters with singles and doubles (CCSD) and 1.5 for multireference second order perturbation theory based on a complete active space self-consistent field reference function (MRPT2). We discuss the results in terms of the pros and cons of each of these methods. Ó 2017 Elsevier B.V. All rights reserved. 1. Introduction Classical valence bond (VB) theory, which was first formulated in 1927 by Heitler and London [1,2] to describe the bond in a hydrogen molecule, served chemists for many years mainly as a qualitative tool. However, in the past three decades the theory has progressed considerably and become a quantitative tool, com- parable to molecular orbital (MO)-based methods. Important mile- stones in the development of quantitative VB methodology include three classes of methods. One class is based on fully delocalized orbitals, also called overlap-enhanced orbitals (OEOs); in this class, the contributions from ionic VB structures are implicitly involved in covalent structures. This class includes, for example the gener- alized valence bond scheme (GVB) [3–6], the spin-coupled VB scheme (SCVB) [7,8], and the complete active space VB method [9]. The second class is based on strictly localized fragment orbi- tals, including the valence bond self-consistent field (VBSCF) method [10] and various recent developments of higher-level ab initio VB methods such as the breathing orbitals valence bond (BOVB) method [11,12], the VB configuration interaction (VBCI) method [13,14], the VB-second-order perturbation theory (VBPT2) [15,16], density-functional-based VB (DFVB) [17,18], and the VB- Quantum Monte Carlo method [19]. Since nonorthogonal localized orbitals are used in this class of methods, one is able to represent the classical VB theory faithfully. Thus, these methods are regarded as ab initio classical VB, and they are the subject of the present article. The third class is the block localized wave function (BLW) approach [20–23], and its extension to the MOVB approach http://dx.doi.org/10.1016/j.comptc.2017.05.031 2210-271X/Ó 2017 Elsevier B.V. All rights reserved. ⇑ Corresponding author at: Institute for Drug Research, School of Pharmacy, Faculty of Medicine, The Hebrew University of Jerusalem, Jerusalem, 91120, Israel. E-mail address: avitalsh@ekmd.huji.ac.il (A. Shurki). Computational and Theoretical Chemistry xxx (2017) xxx–xxx Contents lists available at ScienceDirect Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc Please cite this article in press as: I. Karach et al., Assessing the performance of ab initio classical valence bond methods for hydrogen transfer reactions, Comput. Theoret. Chem. (2017), http://dx.doi.org/10.1016/j.comptc.2017.05.031