Comment on “Intermolecular interaction potentials of the methane dimer from the local density
approximation”
Arvin Huang-Te Li and Sheng D. Chao*
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan, Republic of China
共Received 24 August 2005; published 18 January 2006兲
To verify the recently calculated intermolecular interaction potentials of the methane dimer within the density functional theory using the共Perdew兲 local density approximation 共LDA兲 关Chen et al., Phys. Rev. A 69, 034701 共2004兲兴, we have performed a parallel series of calculations using the LDA/6-311+ +G 共3df, 3pd兲 level of theory with selected exchange functionals共B, G96, MPW, O, PBE, PW91, S, and XA兲. None of the above calculated intermolecular interaction potentials from the local density approximation reproduce the results reported in the commented paper. In addition, we point out the inappropriateness of using the Lennard-Jones function to model the long-range parts of the calculated intermolecular interaction potentials, as sug-gested positively by Chen et al.
DOI:10.1103/PhysRevA.73.016701 PACS number共s兲: 34.20.Gj, 31.15.Ar, 71.15.Mb
Chen et al.关1兴 recently reported the intermolecular inter-action potentials of the methane dimer 共CH4兲2 within the standard density functional theory 共DFT兲 scheme 关2兴 using the 共Perdew兲 local density approximation 共LDA兲 关3兴, the pseudopotential 关4,5兴, and the plane-wave expansion 关6兴. Their results agreed surprisingly well with those obtained by the correlation-corrected Møller-Plesset共MP2, MP3兲 关7兴 and coupled cluster关CCSD共T兲兴 关8兴 methods using a large basis set关9兴. Because it has been known for some time that the usual DFT based approaches, using either the LDA or the generalized gradient approximation共GGA兲, cannot calculate the intermolecular interaction potentials of molecular dimers to such a high level of accuracy关10–12兴, it is important to perform a parallel series of calculations using the available implementations of commonly used exchange-correlation functionals to verify the proposed results by Chen et al.
All the calculations were performed using the GAUSSIAN03 package suite 关13兴 and followed a theoretical procedure similar to that employed by Tsuzuki et al. 关9兴. Figure 1 shows the calculated interaction potentials of 共CH4兲2 with a set of selected exchange functionals共B, G96, MPW, O, PBE, PW91, S, and XA兲 关14兴, together with the Perdew correlation functional dubbed as PL共Perdew local兲 关3兴. Although we have used a pretty large basis set, 6-311+ + G 共3df, 3pd兲, which has been shown to lead to convergent results for 共CH4兲2 at a chemical accuracy 关15兴, none of the calculated intermolecular interaction potentials reproduce the results of Chen et al. A puzzling point in the commented paper is that there are two sets of data, one re-ported in their Fig. 1 and the other as numerical data in the text 关1兴, while the latter is twice the former. Because there was no further clarification on this apparent inconsistency in the commented paper, we present both data for comparison in Fig. 1共open symbol-lines兲. Restated, neither of them can be reproduced in the present calculations.
Chen et al. also concluded that through a nonlinear fitting
their calculated intermolecular potentials can be well-described by the Lennard-Jones共LJ兲 potential function
V共R兲 = a R12−
b
R6. 共1兲
Because this conclusion is contrary to what has been be-lieved that results based on the LDA cannot be used to model the long-range dispersion interaction well关16–18兴, the deter-mined accuracy from their calculations remains to be veri-fied. For the sake of comparison, in Fig. 2 we present the calculated raw data and the claimed fitting curve by Chen et al. using their fitting values of a and b 关1兴. To our great surprise, the fitting curve is anything but like the calculated raw data. To clarify this point, we perform a nonlinear fitting of their calculated data to the LJ function and obtain a = 2.09⫻106Å12kcal/ mol, b = 1.84⫻103Å6kcal/ mol, and the fitting is shown in Fig. 2. As expected, although the LJ function can model the strong repulsive part quite well, there is a significant discrepancy from the calculated data for the
*Corresponding author. Email address: [email protected]. ntu.edu.tw
FIG. 1. The calculated intermolecular interaction potentials us-ing a series of exchange-correlation functionals. The open symbol-lines are the two sets of data taken from Fig. 1 and the text of Ref. 关1兴, respectively. The closed symbol-lines are calculated in the present work using a combination of the selected exchange func-tionals with the Perdew correlation functional.
PHYSICAL REVIEW A 73, 016701共2006兲
long-range interaction part共R⬎4Å兲. The calculated data us-ing the LDA often decays faster than −1 / R6 for the long-range part, due to the local nature of the functionals used. To demonstrate this point, we perform another nonlinear fitting using the exponential function
V共R兲 = Ae−␣R− Be−R 共2兲 and obtain A = 1.14⫻106kcal/ mol, ␣= 4.23 Å−1, B = 3.33⫻102kcal/ mol, and= 1.71 Å−1. As can be seen in Fig. 2, the long-range part of the calculated data is well-modeled by the fast-decaying exponential function, but not the LJ function.
To sum up this comment, the proposed calculated inter-molecular interaction potentials of the methane dimer by Chen et al. cannot be reproduced using the available imple-mentations of the LDA functionals. The calculated data can-not be used to model long-range dispersion interactions of the methane dimer either. We call for a careful examination and cautious usage of the calculated potentials by Chen et al..
This work was supported by the National Science Council of Taiwan, ROC 共NSC-93-2119-M-002-036,NSC-94-2113-M-002-016兲. We acknowledge the National Center for High-performance Computing for providing computing resources. We would like to thank J. C. Jiang and M. Hayashi for useful discussions.
关1兴 X. R. Chen, Y. L. Bai, J. Zhu, and X. D. Yang, Phys. Rev. A
69, 034701共2004兲.
关2兴 R. G. Parr and W. Yang, Density-Functional Theory of Atoms
and Molecules共Clarendon, Oxford, 1989兲.
关3兴 J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 共1981兲. 关4兴 N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 共1991兲. 关5兴 L. Kleinman and D. M. Bylander, Phys. Rev. Lett. 48, 1425
共1982兲.
关6兴 M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 1045共1992兲.
关7兴 C. Møller and M. S. Plesset, Phys. Rev. 46, 618 共1934兲. 关8兴 J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Chem.
Phys. 87, 5968共1987兲.
关9兴 S. Tsuzuki, T. Uchimaru, M. Mikami, and K. Tanabe, Chem. Phys. Lett. 287, 202共1998兲.
关10兴 X. Wu, M. C. Vargas, S. Nayak, V. Lotrich, and G. Scoles, J.
Chem. Phys. 115, 8748共2001兲.
关11兴 H. Sabzyan and M. R. Noorbala, J. Mol. Struct.: THEOCHEM
636, 185共2003兲.
关12兴 S. M. Cybulski and C. E. Seversen, J. Chem. Phys. 119, 12704 共2003兲.
关13兴 M. J. Frisch, et al.,GAUSSIAN03 Revision B.04, Gaussian Inc., Pittsburgh, 2003.
关14兴 Gaussian 03 User’s Reference and IOps Reference 共Gaussian Inc., Pittsburgh, 2003兲.
关15兴 S. Tsuzuki, T. Uchimaru, M. Mikami, and K. Tanabe, J. Phys. Chem. A 102, 2091共1998兲.
关16兴 S. Kristyán and P. Pulay, Chem. Phys. Lett. 229, 175 共1994兲. 关17兴 T. van Mourik and R. J. Gdanitz, J. Chem. Phys. 116, 9620
共2002兲.
关18兴 W. Kohn, Y. Meir, and D. E. Makarov, Phys. Rev. Lett. 80, 4153共1998兲.
FIG. 2. Comparison of the calculated data in Ref.关1兴 with the fittings using the LJ function and the exponential function. The original fitting by Chen et al. is also presented for comparison.
COMMENTS PHYSICAL REVIEW A 73, 016701共2006兲
