Scaled MP2 Method Research Articles

Proposing ab initio assisted lattice distortion theory for phase equilibrium: Pure and mixed refrigerant gas hydrates

AbstractWith promising applications in cold storage and seawater desalination, various refrigerant gas hydrates are experimentally studied for their phase equilibrium behavior; however, the theoretical modeling to predict their formation conditions is under development. Although a high degree of lattice distortion is expected in these gas hydrates due to highly polar and nonspherical molecules of refrigerants, this issue is not addressed in the van der Waals–Platteeuw theory. With this research gap, we formulate a lattice distortion theory for both pure and mixed refrigerant hydrates. For the first time, ab initio methodology comprising the spin‐component scaled MP2 method with Dunning's basis set is implemented for estimating cavity potential of refrigerant hydrates. The extent of lattice distortion is documented in terms of reference chemical potential and enthalpy differences, which are obtained by regressing the Holder's equation with the experimental data of refrigerant hydrate formation. A critical observation is made that the reference properties linearly vary with the “Boltzmann weighted energy‐well depth” of the guest. Analyzing the accuracy of the model using average absolute relative deviation between experimental and predicted pressure of hydrate formation, the proposed lattice distortion model outperforms the existing thermodynamic models for variety of pure and mixed refrigerant hydrates.

Generalized spin-ratio scaled MP2 method for accurate prediction of intermolecular interactions for neutral and ionic species.

The accurate calculation of intermolecular interactions is important to our understanding of properties in large molecular systems. The high computational cost of the current "gold standard" method, coupled cluster with singles and doubles and perturbative triples (CCSD(T), limits its application to small- to medium-sized systems. Second-order Møller-Plesset perturbation (MP2) theory is a cheaper alternative for larger systems, although at the expense of its decreased accuracy, especially when treating van der Waals complexes. In this study, a new modification of the spin-component scaled MP2 method was proposed for a wide range of intermolecular complexes including two well-known datasets, S22 and S66, and a large dataset of ionic liquids consisting of 174 single ion pairs, IL174. It was found that the spin ratio, ϵΔs=EINTOSEINTSS, calculated as the ratio of the opposite-spin component to the same-spin component of the interaction correlation energy fell in the range of 0.1 and 1.6, in contrast to the range of 3-4 usually observed for the ratio of absolute correlation energy, ϵs=EOSESS, in individual molecules. Scaled coefficients were found to become negative when the spin ratio fell in close proximity to 1.0, and therefore, the studied intermolecular complexes were divided into two groups: (1) complexes with ϵΔs< 1 and (2) complexes with ϵΔs≥ 1. A separate set of coefficients was obtained for both groups. Exclusion of counterpoise correction during scaling was found to produce superior results due to decreased error. Among a series of Dunning's basis sets, cc-pVTZ and cc-pVQZ were found to be the best performing ones, with a mean absolute error of 1.4 kJ mol-1 and maximum errors below 6.2 kJ mol-1. The new modification, spin-ratio scaled second-order Møller-Plesset perturbation, treats both dispersion-driven and hydrogen-bonded complexes equally well, thus validating its robustness with respect to the interaction type ranging from ionic to neutral species at minimal computational cost.

Scaled Opposite Spin Second Order Møller−Plesset Theory with Improved Physical Description of Long-Range Dispersion Interactions

Separate scaling of the same-spin and opposite spin contributions to the second-order Møller-Plesset energy can yield statistically improved performance for a variety of chemical problems. If only the opposite spin contribution is scaled, it is also possible to reduce the computational complexity from fifth order to fourth order in system size, with very little degradation of the results. However neither of these scaled MP2 energies recovers the full MP2 result for the dispersion energy of nonoverlapping systems. This deficiency is addressed in this work by using a distance-dependent scaling of the opposite spin correlation energy. The resulting method is compared against the previously proposed scaled MP2 methods on a range of problems involving both short and long-range interactions.

Accurate Calculation of the Heats of Formation for Large Main Group Compounds with Spin-Component Scaled MP2 Methods

Three MP2-type electron correlation treatments and standard density functional theory (DFT) approaches are used to predict the heats of formation for a wide variety of different molecules. The SCF and MP2 calculations are performed efficiently using the resolution-of-the-identity (RI) approximation such that large basis set (i.e., polarized valence quadruple-zeta quality) treatments become routinely possible for systems with 50-100 atoms. An atom equivalent scheme that corrects the calculated atomic energies is applied to extract the "real" accuracy of the methods for chemically relevant problems. It is found that the spin-component-scaled MP2 method (SCS-MP2, J. Chem. Phys, 2003, 118, 9095) performs best and provides chemical accuracy (MAD of 1.18 kcal/mol) for a G2/97 test set of molecules. The computationally more economical SOS-MP2 variant, which retains only the opposite-spin part of the correlation energy, is slightly less accurate (MAD of 1.36 kcal/mol) than SCS-MP2. Both spin-component-scaled MP2 treatments perform significantly better than standard MP2 (MAD of 1.77 kcal/mol) and DFT-B3LYP (MAD of 2.12 kcal/mol). These conclusions are supported by results obtained for a second test set of complex systems containing 70 molecules, including charged, strained, polyhalogenated, hypervalent, and large unsaturated species (e.g. C60). For this set, DFT-B3LYP performs badly (MAD of 8.6 kcal/mol) with many errors >10-20 kcal/mol while the spin-component-scaled MP2 methods are still very accurate (MAD of 2.8 and 3.7 kcal/mol, respectively). DFT-B3LYP shows an obvious tendency to underestimate molecular stability as the system size increases. Out of six density functionals tested, the hybrid functional PBE0 performs best. All in all, the SCS-MP2 method, together with large AO basis sets, clearly outperforms current DFT approaches and seems to be the most accurate quantum chemical model that routinely can predict the thermodynamic properties of large main group compounds.

Spin-component scaled second-order Møller–Plesset perturbation theory for the calculation of molecular geometries and harmonic vibrational frequencies

The implementation and performance of an analytic gradient with respect to nuclear displacements for the spin-component scaled MP2 method (SCS-MP2) is presented. The geometries and vibrational frequencies of a benchmark set of 31 first-row molecules are considered. The new SCS-MP2 method performs significantly better than standard MP2: the RMS deviation (mean absolute error) for bond lengths drops from 1.2 (0.8) to 0.9 (0.6) pm and from 84 (67) to 57 (48) cm −1 for the vibrational frequencies. As further tests the geometries of weakly bonded systems, transition metal compounds and organic transition states are considered. For almost all systems the SCS-MP2 method outperforms the MP2 approach albeit for the same computational cost. Significant improvements are especially observed for cases which are usually known as MP2 pitfalls.