Gershom (Jan M.L.) Martin
Department of Organic Chemistry
Weizmann Institute of Science
7610001 Reḥovot, Israel
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While density functional theory has made great strides, even the best exchange-correlation functionals are about one order of magnitude less accurate than can be achieved using modern wavefunction ab initio techniques. The latter have a well-defined road map for refinement in accuracy; however, their steep computational cost scaling with system size limits their use to relatively small molecules. While some applications (e.g., atmospheric chemistry, fine thermochemistry) demand such levels of accuracy, a perhaps more important application is the creation of benchmark datasets for the parametrization and validation of density functional, reactive force fields, and other lower-cost methods.
Using the case of total atomization energies, we will discuss the breakdown of molecular binding energies into their constituent components, as well as the optimal convergence strategy for each. By such “layered approximations” as implemented in the Weizmann-n series of thermochemistry protocols [1,2,3] (and its ‘competitor’, the HEAT approach ), CPU times and memory requirements can be drastically reduced versus brute-force approaches. The introduction of explicitly correlated coupled cluster theory brings still larger molecules within reach, as long as non dynamical correlation effects are not too important. (See  for a discussion of static correlation diagnostics.)
We will illustrate some of the concepts using the W4-11 atomization energy benchmark , the DBH24 barrier heights benchmark , the HFREQ27 vibrational frequencies benchmark , and several recent benchmarks for noncovalent interactions such as the S66x8 set of biomolecule dimer potentials, , conformational energies of the proteinogenic amino acids, , and water clusters .
 Amir Karton, Elena Rabinovich, Jan M.L. Martin*, and Branko Ruscic, "W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions", Journal of Chemical Physics 125, 144108 (2006) [DOI: 10.1063/1.2348881] [PDF Courtesy of Publisher]
 Amir Karton, Peter R. Taylor, and Jan M. L. Martin, "Basis set convergence of post-CCSD contributions to molecular binding energies", Journal of Chemical Physics 127, 064104 (2007) [DOI: 10.1063/1.2755751]. [PDF Courtesy of Publisher]
 Nitai Sylvetsky, Kirk A. Peterson, Amir Karton,and Jan M. L. Martin, "Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled?", Journal of Chemical Physics 144, 214101 (2016). [DOI: 10.1063/1.4952410]
 Michael E. Harding, Juana Vázquez, Branko Ruscic, Angela K. Wilson, Jürgen Gauss, and John F. Stanton, “High-Accuracy Extrapolated Ab Initio Thermochemistry. III. Additional Improvements and Overview.” Journal of Chemical Physics 128, 114111 (2008). [DOI: 10.1063/1.2835612]
Diagnostics for nondynamical correlation
 Uma R. Fogueri, Sebastian Kozuch, Amir Karton and Jan M.L. Martin, "A simple DFT-based diagnostic for nondynamical correlation", Theoretical Chemistry Accounts 132, 1291-1299 (2013) [DOI: 10.1007/s00214-012-1291-y] [special collection: Quantum Chemistry in Belgium]
W4-11 and W4-17 benchmark databases
 Amir Karton, Shauli Daon, and Jan M.L. Martin, "W4-11: a high-confidence benchmark dataset for computational chemistry derived from W4 ab initio data", Chemical Physics Letters 510, 165-178 (2011) [Frontiers and cover article; DOI: 10.1016/j.cplett.2011.05.007]; Amir Karton, Nitai Sylvetsky, and Jan M. L. Martin, "W4-17: A diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods", Journal of Computational Chemistry 38, 2063-2075 (2017). [DOI: 10.1002/jcc.24854]
DBH24 barrier heights database
 Amir Karton, Alex Tarnopolsky, Jean-François Lamère, George C. Schatz, and Jan M. L. Martin, "Highly accurate first-principles benchmark datasets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics", Journal of Physical Chemistry A 112, 12868-12886 (2008). [Sason Shaik issue; DOI: 10.1021/jp801805p (subscribers); Supporting information; Request e-reprint (nonsubscribers)].
Benchmarks for (an)harmonic frequencies and zero-point energies
 Jan M. L. Martin and Manoj K. Kesharwani, "Assessment of CCSD(T)-F12 approximations and basis sets for harmonic vibrational frequencies", Journal of Chemical Theory and Computation 10, 2085-2090 (2014). [DOI: 10.1021/ct500174q]. [Get Open Access Article]; Manoj K. Kesharwani, Brina Brauer, and Jan M. L. Martin, "Frequency and zero-point vibrational energy scale factors for double hybrid density functionals (and selected other methods): can anharmonic force fields be avoided?", Journal of Physical Chemistry A 119, 1701-1714 (2015). [Special issue: 25th Austin Symposium on Molecular Structure and Dynamics. DOI: 10.1021/jp508422u]
F12 benchmarks for non covalent interactions
 Brina Brauer, Manoj K. Kesharwani, Sebastian Kozuch, and Jan M. L. Martin, "The S66x8 benchmark for noncovalent interactions revisited: explicitly correlated ab initio methods and density functional theory", Physical Chemistry Chemical Physics A 18, 20905–20925 (2016). [DOI: 10.1039/C6CP00688D] [Get Open Access Article and journal back cover] [Part of themed issue: Developments in Density Functional Theory]
 Manoj K. Kesharwani, Amir Karton, and Jan M. L. Martin, "Benchmark ab initio conformational energies for the proteinogenic amino acids through explicitly correlated methods. Assessment of density functional methods", Journal of Chemical Theory and Computation 12, 444-454 (2016). [DOI: 10.1021/acs.jctc.5b01066
 Debashree Manna, Manoj Kumar Kesharwani, Nitai Sylvetsky, and Jan M. L. Martin, "Conventional and explicitly correlated ab initio benchmark study on water clusters: revision of the BEGDB and WATER27 datasets", Journal of Chemical Theory and Computation 13, 3136-3152 (2017). [DOI: 10.1021/acs.jctc.6b01046]