HM-IE: Quantum Chemical Hybrid Methods for Calculating Interaction Energies Jeffery B. Klauda, Stephen L. Garrison, Jianwen Jiang, Gaurav Arora, and Stanley I. Sandler* Department of Chemical Engineering, Center for Molecular and Engineering Thermodynamics, UniVersity of Delaware, Newark, Delaware 19716 ReceiVed: June 10, 2003; In Final Form: September 2, 2003 Accurate intermolecular potentials are needed for quantitative molecular simulations, but their calculation from quantum mechanics can be very demanding. We have developed several variations of a procedure, which we collectively refer to as quantum mechanical Hybrid Methods for Interaction Energies (HM-IE), to accurately estimate interaction energies from CCSD(T) calculations with a large basis set (LBS). HM-IE was tested for interaction energies of Ne 2 , (C 2 H 2 ) 2 , and N 2 -benzene for many orientations sampling the entire potential energy surface and was found to be in excellent agreement with the CCSD(T)/LBS results while requiring considerably less computational time and resources. Furthermore, for neon, an intermolecular potential fit to interaction energies using HM-IE and a potential fit to CCSD(T)/LBS energies resulted in nearly identical predictions for densities and vapor pressures. Introduction Molecular simulations have been used to predict a broad range of physical and thermodynamic properties, including protein- folding dynamics, 1-3 gas transport properties in nanostructures, 4-7 and phase behavior. 8,9 Quantum mechanics (QM) can be used to develop the intermolecular potentials (IP) necessary to accurately calculate properties from simulation. However, calculations of the interaction energies between molecules require approximations to the Hamiltonian and wave function. Dunning 10 investigated approximations such as HF, MP2, MP4, and CCSD(T) for various types of molecular interactions. In that work, the MP2 method was found to accurately predict measured binding energies for hydrogen-bonded systems and led to reasonable agreement for weakly bound molecules (interaction energies from a few kcal/mol to a fraction of a kcal/ mol). However, only the CCSD(T) method resulted in an accurate representation of the binding energies for very weakly bounded systems (less than a tenth of a kcal/mol). 10 In addition, CCSD(T) is known to be required for accurate interactions in other systems, e.g., aromatic systems. 11 Moreover, these levels of accuracy were only achieved when a large basis set was used to accurately represent the electronic wave function, but the use of CCSD(T) with a large basis set (LBS) is computationally very demanding. Hybrid or compound QM methods, such as the Gaussian-3 (G3) methods developed by Curtiss et al. 12,13 and those of Dunning and Peterson, 14 have been used to successfully estimate molecular properties by assuming that the separate effects of electron correlation and basis set size are additive. In the G3 methods, high level energy calculations, e.g., QCISD(T), are performed with small basis sets, and lower level calculations (MP2 and MP4) are performed with larger basis sets. These calculated results are then combined, resulting in accurate heats of formation, ionization potentials, electron affinities, and proton affinities to within (8 kJ/mol with relatively fast calculations compared to QCISD(T) with large basis sets. Dunning and Peterson 14 also approximated the basis set dependence of CCSD(T) calculations with that of Møller-Plesset perturbation methods for various properties, e.g., dissociation energies, harmonic frequencies, and ionization potentials. 14 This method resulted in average absolute errors of less than 1.7 kJ/mol, 2 cm -1 , and 0.42 kJ/mol for dissociation energies, harmonic frequencies, and ionization potentials, respectively. For interaction energies, several authors 15-18 have used MP2 to approximate the CCSD(T) energy at the basis set limit, i.e., the value from CCSD(T) with an infinitely sized basis set. This was done by calculating MP2 energies with several large basis sets, extrapolating to the basis set limit, and then combining this extrapolation with a CCSD(T) interaction energy calculated using only a small or moderately sized basis set. Similarly, for a small number of orientations and a single separation distance, Tsuzuki et al. 11 and Koch et al. 19 approximated CCSD(T)/LBS energies by calculating CCSD(T) with a smaller basis set and added to this result a correction based on the difference between MP2 energies with a LBS and a smaller basis set. However, this approximation for benzene-benzene interactions at CCSD(T)/ aug(d)-6-311g* by Tsuzuki et al. 11 resulted in errors of 0.5- 1.4 kJ/mol for the three orientations and the single separation distance they studied. In addition, an accurate approximation of the CCSD(T)/aug-cc-pVQZ interaction energies for benzene- argon studied by Koch et al. 19 still required the use of a reasonably large basis set (aug-cc-pVTZ) for the small basis set (SBS). Presented here is a class of QM hybrid methods referred to as HM-IE (Hybrid Methods for Interaction Energies) that accurately approximates interaction energies calculated with CCSD(T) and a LBS, but requires considerably less computa- tional time and resources. In HM-IE, an approach similar to that of the G3 methods, 12,13 Dunning and Peterson, 14 and others 11,15-19 is used, which assumes that the effects of electron correlation and basis set size are additive. However, unlike Tsuzuki et al. 11 and Koch et al., 19 several hybrid methods to approximate CCSD(T)/LBS results were investigated for three different systems and a wide range of orientations and separation * To whom correspondence should be addressed. Phone: (302) 831- 2945. Fax: (302) 831-3226. E-mail: sandler@udel.edu. 107 J. Phys. Chem. A 2004, 108, 107-112 10.1021/jp035639e CCC: $27.50 © 2004 American Chemical Society Published on Web 12/05/2003