A fast hybrid method for constructing multidimensional potential energy surfaces from ab initio calculations: A new global analytic PES of NH 2 system Huanchen Zhai, Shi Ying Lin ⇑ School of Physics, Shandong University, Jinan 250100, China article info Article history: Received 16 December 2014 In final form 11 April 2015 Available online 28 April 2015 Keywords: Potential energy surface Quantum reaction dynamics Interpolation Wave packet abstract A hybrid fitting scheme is proposed for the construction of global analytic ab initio potential energy sur- faces (PESs) by means of applying reproducing kernel Hilbert space (RKHS) interpolation and cubic spline interpolation onto different dimensions of the molecular configuration space. In addition to inheriting most advantages of the pure RKHS method, this scheme offers the following extra benefits: short initia- tion time and enhanced stability and accuracy. We also propose a fast algorithm for the scheme allowing the PES computation time to be independent of the number of ab initio points. We have constructed an adiabatic PES of N( 2 D) + H 2 ?NH + H reactive system from more than twenty thousand ab initio points using this scheme. The accurate quantum dynamics results calculated on the constructed PES demon- strate high accuracy and efficiency of this new scheme. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction The construction of a global analytic potential energy surface (PES) from the fitting of discrete ab initio points is an essential step to perform a theoretical simulation of molecular dynamics. Direct dynamics approach which is able to avoid the fitting procedure by supplying the PES values on the fly, is yet computationally impractical. A large number of studies have been devoted over the past decades in an effort to design efficient fitting schemes [1–4]. Traditional approaches are mostly based on a least squares fitting of discrete ab initio points invoking system-specific ad hoc functional forms. The system-specificity limits the generality of such method and moreover it is often not an easy task to design a suitable functional form appropriate for the system of interest. Thus the methods based on generic algorithms are constantly pur- sued and notable progresses along this direction have been made recently. These algorithms include cubic splines [5–7], interpolat- ing moving least-squares [8–10], neural networks [11–15], modi- fied Shepard interpolation [16], reproducing kernel Hilbert space [17], and permutationally invariant methods [3,15,18], just to mention a few. Perhaps the most popular one that belongs to this category is the cubic spline method [5–7], which can produce an accurate PES, if a large number of ab initio points are provided. When the available ab initio points are sparse, the generated PES often suffers from spurious oscillatory features. Due to the requirement of large ab initio points, this method is hard to apply to systems of more than three dimensions. Recently, Ho et al. proposed [17] a novel interpolation method based on reproducing kernel Hilbert space (RKHS) theory. The RKHS method has been proved to be able to construct high-quality PESs with many remarkable advantages [17,19,20], such as, guaranteed correct symmetry properties and asymptotic behavior of the molecular system, and the availability of analytic derivatives of the molecular PES. The same authors also proposed a fast algorithm of the RKHS method so that the compu- tations for the PES and its derivatives can be greatly accelerated [21]. (This fast version will be referred to as the fast RKHS here- after.) Therefore the PESs constructed using this method is suitable for quantum dynamical as well as quasiclassical trajectory studies. However, the implementation of this method may become highly tricky when a large number of ab initio points are provided, due to the numerical instability of the associated linear inverse prob- lem. In this case, some arbitrary parameters need to be adjusted many times until one gets satisfactory results. For each newly cho- sen parameter set, one needs lengthy initiation time to solve a set of large-sized linear equations. To alleviate this problem, we propose a new hybrid scheme for the construction of a smooth PES from ab initio points. By applying RKHS interpolation and cubic spline interpolation onto different http://dx.doi.org/10.1016/j.chemphys.2015.04.012 0301-0104/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: sylin@sdu.edu.cn (S.Y. Lin). Chemical Physics 455 (2015) 57–64 Contents lists available at ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys