Comparative study of electronic-structure methods for platinum-containing molecules: bond lengths and bond dissociation energies

Eur. Phys. J. D (2019) 73: 135 https://doi.org/10.1140/epjd/e2019-90691-1 THE EUROPEAN PHYSICAL JOURNAL D Regular Article Comparative study of electronic-structure methods for platinum-containing molecules: bond lengths and bond dissociation energies?,?? Daniel Süß, Stefan E. Hubera , and Andreas Mauracherb Institute of Ion Physics and Applied Physics, University of Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria Received 19 December 2018 / Received in final form 3 April 2019 Published online 2 July 2019 c The Author(s) 2019. This article is published with open access at Springerlink.com Abstract. We compare various electronic structure methods including a broad range of density functionals with experimental data on bond lengths and bond dissociation energies available for di- and triatomic platinum-containing molecules. In total we employ 54 GGA, 17 meta-GGA, 36 hybrid, 103 mixed GGA/meta GGA, 17 hybrid, 7 meta hybrid, 10 range-separated hybrid and 5 double hybrid density functionals. Furthermore, the performance of ab initio methods including Hartree-Fock, Møller-Plesset perturbation theory up to fourth order as well as coupled cluster theory up to perturbatively approximated triple excitations, i.e. CCSD(T), is also investigated. In the case of bond lengths, the smallest mean average deviation from experimental values yielding 0.3 pm is found for the hybrid density functional TPSSh. Interestingly, neither recent double hybrid functionals nor ab initio methods result in similar, commensurable accuracies. For the investigated bond dissociation energies, the GGA functional TPSSVWN5 is the closest to experiment with deviations of 6.97 kcal/mol. Finally, we address various possible sources of errors that may explain the large mean average deviation from experiment in the case of CCSD(T) (8.87 kcal/mol), including the effect of basis set size, the influence of the multireference character of the molecular wave function, the quality of the HF determinant as reference wave function and the influence of core electron correlation. 1 Introduction Platinum containing molecules are up to now among the leading drugs used in anticancer chemotherapy and cover substances such as cisplatin (cis-diamminedichloridoplati num(II)), carboplatin (cis-diammine(cyclobutane-1,1-dica rboxylate-O,O’)platinum(II)), oxaliplatin ([(1R,2R)-cl ocyhexane-1,2-diamine](ethanedioato-O,O’)platinum(II)) and many more [1]. Despite the clinical usefulness of those so far developed and approved cytostatic agents, they still exhibit major drawbacks which restrict their usage. Dose-limiting side effects include nephrotoxicity, ototoxicity and neurotoxicity, high reactivity and limited solubility, intrinsic and/or acquired resistances and the uncomfortable and cost intensive way of administration via infusion [2]. Unsurprisingly, much research has been devoted to overcome these limitations [3,4]. Even a restricted scan of only platinum-containing molecules ? Contribution to the Topical Issue “Dynamics of Systems on the Nanoscale (2018)”, edited by Ilko Bald, Ilia A. Solov’yov, Nigel J. Mason and Andrey V. Solov’yov. ?? Supplementary material in the form of one pdf file available from the Journal web page at https://doi.org/10.1140/epjd/e2019-90691-1 a e-mail: b e-mail: has still to cover a vast variety of possible candidate molecules. Therefore, providing as good as possible theoretical and/or empirical guidance for a systematic design of considered drugs appears essential. In particular, in order to design metal-organic drugs with improved pharmacological profiles, details of the modes of action, toxicity and resistance need to be studied, understood and linked to underlying molecular properties. Thus, relations may be discovered which reveal how properties at the microscopic, i.e. molecular, level and the macroscopic one, i.e. the efficacy of a considered drug in clinical research, are connected. Such approaches are well-established in pharmaceutical research, e.g. in form of (quantitative) structure-activity relationship (QSAR or SAR) and related theoretical studies which have been applied also in the present context [2,5,6]. However, the outcome of such studies depends heavily on the reliability and validity of the numerical, typically quantum chemical, methods employed to compute properties at the molecular level. In general, computational chemistry offers a broad variety of methods which vary substantially in both achievable accuracy as well as computational cost depending on the size of the chemical system under consideration. For system sizes typical for the research framework described above, a viable balance between reasonable accuracy and manageable computational cost is delivered Page 2 of 9 by density functional theory (DFT). The validation of DFT for a certain application requires comparison of representative molecular properties to reliable experimental or higherlevel theoretical data or both. For main group chemistry, coupled cluster (CC) theory provides such higher-level theoretical methods which are able to deliver benchmarkquality data [7]. Especially CC including single and double excitations with a quasi-perturbative treatment of connected triple excitations, i.e. CCSD(T) [8,9], became known as a “gold standard” in computational chemistry due to its often delivered high accuracy. In the light of the scarcity of reliable experimental molecular properties for systems containing transition metals like platinum, it therefore appears appropriate to use reference data derived by CCSD(T) in order to validate computationally less demanding DFT approaches. Unfortunately, the situation is more difficult and controversial in this case than for main group chemistry. Whereas Truhlar and co-workers [10] showed that CCSD(T) does not generally deliver benchmark quality data for systems containing transition metals, Dixon and co-workers [11] could scrutinize the importance of the inclusion of core electrons and extrapolation to the complete basis set (CBS) limit in order to achieve this goal. In this work, we revise some of these findings by comparison of results obtained with diverse electronic-structure methods with available experimental gas-phase data on molecular geometries and energies, however focusing specifically on platinum-containing molecules. In particular, we compare the results of various ab initio approaches (from Hartree-Fock (HF) theory up to CCSD(T)) as well as DFT methods (including GGA, meta GGA, hybrid, meta hybrid, range-separated hybrid and double hybrid functionals) with experimental data for ten bond lengths and ten bond dissociation energies (BDEs) of di- and triatomic platinumcontaining molecules. Although admittedly small, the size of our test sets for these molecular properties reflects the scarcity of available experimental data. To the best of our knowledge, no such gas-phase data for the larger anticancer compounds have been reported so far. Note that is s (...truncated)