1 3 Theor Chem Acc (2014) 133:1544 DOI 10.1007/s00214-014-1544-z REGULAR ARTICLE Quantitative estimation of uncertainties from wavefunction diagnostics Matthew K. Sprague · Karl K. Irikura Received: 26 September 2013 / Accepted: 12 July 2014 / Published online: 7 August 2014 © Springer-Verlag Berlin Heidelberg (outside the USA) 2014 1 Introduction Theoretical predictions of ideal-gas molecular energet- ics are commonplace. The most popular theory in quan- titative work is coupled-cluster theory with a perturbative correction, CCSD(T) [1, 2]. This is applied together with a large one-electron basis set, or a series of sets that can be extrapolated to the limit of a complete basis set (CBS). This practice has been summarized by Dunning [3], Peter- son [4], Feller [5], and Dixon [6], to name a few. More recently, “explicitly correlated” treatments of electron cor- relation [7] have become easy to use. These new methods perform markedly better than conventional calculations for basis sets of similar size, reaching the CBS limit faster than traditional methods [8, 9]. Following the model of Dunning’s correlation-consistent basis sets, new basis sets have been developed specifically for explicitly correlated calculations [8]. In some cases, CCSD(T) predictions are noticeably less accurate than usual. Examples include F 2 , O 3, and transition metal compounds [10, 11]. Often, this is because Hartree– Fock (HF) theory produces such a poor description of the electronic structure that CCSD(T), which is built atop the HF wavefunction, is unable to compensate. To detect this problem, many wavefunction diagnostics have been pro- posed. Examples include the T 1 and D 1 diagnostics by Lee and coworkers [12, 13]; the B1, GB1, ROD, and M diag- nostics by Truhlar and co-workers [14–16]; %TAE[(T)] by Martin and co-workers [17]; and the natural orbital occupation number diagnostic developed by Gordon and co-workers [18]. Recently, a diagnostic for hybrid density functional theory has been proposed by Fogueri et al. [19] based upon the dependence of atomization energies upon the mixing coefficient. The informatics analysis derived from density matrix renormalization group methods also Abstract Coupled-cluster calculations with large basis sets are used widely to make predictions of gas-phase ther- mochemistry. Wavefunction diagnostics are sometimes used to indicate whether or not there is problematic multi- reference character that may cause errors. Here, we inves- tigate whether existing diagnostics, as well as diagnos- tics proposed by us, can be used to estimate these errors quantitatively. We calculate the atomization energy of 50 molecules, including known multireference molecules such as CN, C 2 , O 3 , ortho-benzyne, formaldehyde oxide, and hydrogen trioxy radical. In addition to the c 0 2 , T 1 , D 1 , and %TAE[(T)] diagnostics, we assess the Hartree–Fock HOMO–LUMO gap, maximum occupation number defect, first vertical excitation energy, a direct estimate of multiref- erence effects, and combinations of diagnostics as indica- tors of errant thermochemistry. Keywords T 1 · D 1 · %TAE[(T)] · Atomization energy · Non-dynamical correlation · Thermochemistry Dedicated to Professor Thom Dunning and published as part of the special collection of articles celebrating his career upon his retirement. Electronic supplementary material The online version of this article (doi:10.1007/s00214-014-1544-z) contains supplementary material, which is available to authorized users. M. K. Sprague · K. K. Irikura (*) Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8320, USA e-mail: karl.irikura@nist.gov M. K. Sprague e-mail: matthew.sprague@nist.gov