Article pubs.acs.org/JPCA
Assessment of the Performance of MP2 and MP2 Variants for the Treatment of Noncovalent Interactions Kevin E. Riley,*,† James A. Platts,‡ Jan Ř ezác,̌ † Pavel Hobza,†,§ and J. Grant Hill∥ †
Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Czech Republic School of Chemistry, Cardiff University, Park Place, Cardiff CF10 3AT, United Kingdom § Regional Center of Advanced Technologies and Materials, Department of Physical Chemistry, Palacky University, 771 46 Olomouc, Czech Republic ∥ School of Chemistry, University of Glasgow, Joseph Black Building, University Avenue, Glasgow G12 8QQ, United Kingdom ‡
S Supporting Information *
ABSTRACT: For many years, MP2 served as the principal method for the treatment of noncovalent interactions. Until recently, this was the only technique that could be used to produce reasonably accurate binding energies, with binding energy errors generally below ∼35%, at a reasonable computational cost. The past decade has seen the development of many new methods with improved performance for noncovalent interactions, several of which are based on MP2. Here, we assess the performance of MP2, LMP2, MP2-F12, and LMP2-F12, as well as spin component scaled variants (SCS) of these methods, in terms of their abilities to produce accurate interaction energies for binding motifs commonly found in organic and biomolecular systems. Reference data from the newly developed S66 database of interaction energies are used for this assessment, and a further set of 38 complexes is used as a test set for SCS methods developed herein. The strongly basis set-dependent nature of MP2 is confirmed in this study, with the SCS technique greatly reducing this behavior. It is found in this work that the spin component scaling technique can effectively be used to dramatically improve the performance of MP2 and MP2 variants, with overall errors being reduced by factors of about 1.5−2. SCS versions of all MP2 variants tested here are shown to give similarly accurate overall results.
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INTRODUCTION It is widely recognized that the accurate description of noncovalent interactions is critical in many areas of chemistry, biology, and material science.1−6 For several decades, there was only one technique available to the computational chemist that could give reasonably accurate interaction energy results at a feasible computational cost, MP2.2,5 This method has been used extensively throughout the years for the treatment of noncovalent interactions in a large variety of molecular systems. The past decade has seen the development of a wide variety of new methods aimed at describing these interactions more accurately and at a lower computational cost. Examples of such methods are density functional theory with empirical dispersion corrections (DFT-D),7−9 the exchange-hole dipole moment technique (XDM),10 dispersion corrected semiempirical methods (AM1-D, PM6-D, DFTB-D),11−13 spin component scaled MP2 (SCS-MP2 and SCS-MI-MP2),14−16 MP2.5 (and MP2.X),17,18 and spin component scaled CCSD (SCS-CCSD and SCS-MI-CCSD).19,20 Each of these methods was designed to give the most accurate interaction energies possible at a given computational cost point. It should be noted that each of the methods listed above relies (sometimes greatly) on empirical parameters that must be fit to reference data. MP2 © 2012 American Chemical Society
has the advantage of being a nonempirical, although the choice of basis set can strongly affect its ability to reproduce reference data. The aim of this work is to characterize the interaction energy errors that can be expected from MP2 and other methods based on MP2, including local MP2 (LMP2), explicitly correlated MP2 (MP2-F12), and different variants of SCS based on these. For this purpose, we use the newly developed S66 data set of intermolecular interaction energies, which includes a wide variety of interaction types.21,22 It is well-known that binding energies obtained with MP2 and, to a lesser extent, other MP2based methods are highly dependent on the basis set that is used.23 For this reason, we assess the performance of MP2 along with 14 different basis sets, as well as at the complete basis set limit. Smaller numbers of basis sets, being mainly of intermediate size, are used in assessing the performance of the local and scaled MP2-based methods. The S66 data set was designed to describe the most important binding motifs found in biochemical systems.21,22 Received: December 13, 2011 Revised: March 30, 2012 Published: April 4, 2012 4159
dx.doi.org/10.1021/jp211997b | J. Phys. Chem. A 2012, 116, 4159−4169
The Journal of Physical Chemistry A
Article
correction, was parametrized against the S22 database of intermolecular interaction energies.14 Scaling of the os and ss MP2 terms results in improved interaction energies and yields a more balanced description of hydrogen bonding, aliphatic interactions, and aromatic interactions. In this work, we parametrize new variants of SCS-MI-MP2 to the S66 data set of interaction energies; we refer to these newly parametrized methods as SCS-S66-MP2. As the S66 comprises a more balanced set of noncovalent interaction types than S22, it is expected that SCS-S66-MP2 methods are better able to treat a wider variety of molecular complexes than are the SCS-MIMP2 methods. Local correlation methods such as LMP2 exploit the “nearsighted” nature of electron correlation by carrying out the calculation in a set of localized orbitals.28−30 Only excitations to virtual orbitals that are spatially close to the occupied ones are considered, leading to significant efficiency gains over conventional MP2 calculations. An added advantage of this approach is that excitations that contribute to basis set superposition error (BSSE) are omitted by construction,31−33 making it unnecessary to use counterpoise corrections to account for basis set incompleteness as long as the orbital basis set is sufficiently large to saturate the underlying Hartree−Fock calculation. This makes these methods ideal in geometry optimization of large clusters, or treatment of systems in which intramolecular interactions are important, for which application of the standard counterpoise correction for BSSE is problematic. Explicitly correlated methods such as MP2-F12 circumvent the slow convergence of correlation energy with respect to basis set size by including terms that depend explicitly on the interelectron distance, r12, and hence yield results close to the CBS limit from relatively small basis sets such as aug-cc-pVDZ (for recent reviews of explicitly correlated methods and their performance, see refs 34,35). There have been several studies aimed at assessing the performance of MP2, spin component scaled MP2 variants (SCS-MP2, 15 SCS-MI-MP2, 14 SOS-MI-MP2, 14 SSS-MIMP214), LMP2, and SCSN-MP216,36,37 (based on SCSLMP2), in terms of their abilities to describe noncovalent interactions.23,38−42 Taken together, the results of these assessment studies are that (a) the quality of MP2 results largely depends on the basis set that is employed, (b) SCS scaling generally improves MP2 binding energies substantially, and (c) SCS methods scaled specifically for noncovalent interactions offer improved results over the parent SCS-MP2 method. Here, we test the performance of several MP2-based methods in terms of their abilities to produce accurate binding energies for intermolecular noncovalent interactions in molecular complexes. Assessment of these methods in terms of other properties, such as quality of minimum energy geometries of noncovalent complexes and conformational energies for systems containing intramolecular interactions, will be addressed in future studies.
This set represents a great improvement over the popular S22 data set,24 which places too much emphasis on the cyclic hydrogen bonds and stacked aromatic−aromatic interactions found in nucleic acids. Structures and reference binding energies for the complexes in the S66 set are available online (http://www.begdb.com/).25 One of the main reasons for the relative success (and sometimes, failure) of the MP2 method in describing noncovalent interactions is a compensation of errors that involves, on one hand, the method’s failure to describe intramonomer correlation effects, causing an overall overestimation of dispersion attraction, and, on the other hand, basis set deficiency, which leads to underestimation of the total binding energy. In many circumstances, this compensation of errors is maintained, and the resulting binding energies are reasonably accurate, while in other circumstances (especially for stacked aromatic interactions), the balance between the two compensating factors is shifted, resulting in less accurate binding energies. Please see refs 26 and 27 for more details concerning the origins of the MP2 description of molecular complexes. MP2 generally gives fairly accurate results for intermolecular complexes, but, because its description generally relies on cancellation of errors, results are highly basis set dependent.5,23,27 There is no systematic improvement in MP2 results when the size of the basis set is increased, which makes it necessary to determine which basis sets yield the best results for interaction energies. There are two general properties of MP2 that can be used to aid in the selection of an optimum basis set; these are: (a) Interaction energies for hydrogen bonds and dispersion interactions involving aliphatic molecules become more accurate as the basis set size increases, and the best results are generally obtained with basis sets at least as large as aug-ccpVTZ. (b) Dispersion interactions involving aromatic groups are generally overbound when large basis sets are used; this is especially true for stacked aromatic−aromatic interactions, for which even the (relatively small) aug-cc-pVDZ basis can overbind significantly. Thus, it is necessary to choose a basis set that is large enough to provide a reasonable description of hydrogen bonds and aliphatic−aliphatic interactions but small enough not to strongly overbind interactions involving aromatic groups. In the past, we have recommended that the cc-pVTZ basis represents the best compromise between these two factors, giving reasonable interaction energies for a range of different interaction types. Spin component scaling (SCS) relies on scaling of the MP2 opposite-spin (os) and same-spin (ss) components of the correlation energy.14−16 The original form of SCS, proposed by Grimme, uses a standard set of scaling parameters to improve the MP2 description of a diverse range of properties including thermodynamics and kinetics.15 The basis for the improved description produced by SCS-MP2 is an enhancement of dynamical correlation (os term >1), which is underestimated by MP2, and diminished contributions from geometric (nondynamical) correlation (ss term
