Optimization and Basis-Set Dependence of a Restricted-Open-Shell Form of B2-PLYP Double-Hybrid Density Functional Theory

Abstract

The performance of the restricted-open-shell form of the double-hybrid density functional theory (DHDFT) B2-PLYP procedure has been compared with that of its unrestricted counterpart using the G3/05 test set. Additionally, the influence of basis set on the parametrization and performance of ROB2-PLYP, and the further improvement of ROB2-PLYP through augmentation with a long-range dispersion function, have been investigated. We find that, after optimization of the two empirical DHDFT parameters, the ROB2-PLYP method (HF exchange = 59% and MP2 correlation = 28%) performs slightly better than the corresponding UB2-PLYP method (HF exchange = 62% and MP2 correlation = 35%), with mean absolute deviations (MADs) from the experimental energies in the G3/05 test set of 9.1 and 9.9 kJ mol(-1), respectively, when the cc-pVQZ basis set is employed. Separate optimizations of the parameters for the RO and U procedures are crucial for a fair comparison. For example, for the G2/97 test set, ROB2-PLYP(53,27) and ROB2-PLYP(62,35) show MADs of 12.2 and 13.5 kJ mol(-1), respectively, compared with the 6.6 kJ mol(-1) for (the optimized) ROB2-PLYP(59,28). The performance of ROB2-PLYP deteriorates significantly as the basis-set size is decreased, reflecting the enhanced basis-set dependence of the MP2 contribution compared with standard DFT. We find that this deficiency can be partly overcome through reparametrization. However, when the basis set drops below triple-zeta, the improvements made on reoptimizing the ROB2-PLYP parameters are not sufficient to warrant their general use. We find that the dispersion- and BSSE-corrected ROB2-PLYP(59,28)-D HCP procedure performs significantly better than ROB2-PLYP(59,28) for the S22 test set of interaction energies in which dispersion interactions are particularly important, with the MAD falling from 6.1 to 1.6 kJ mol(-1). However, when the same D correction is applied to the G3/05 test set, the performance of ROB2-PLYP(59,28)-D deteriorates slightly compared with ROB2-PLYP(59,28), with the MAD increasing from 9.1 to 9.5 kJ mol(-1).

A fast doubly hybrid density functional method close to chemical accuracy using a local opposite spin ansatz

“…Equally important is that XYG3 and other DHDFs (15)(16)(17)(18)(19) scale formally with the fifth power of the size, while XYGJ-OS scales formally with the fourth power, and for the local implementation it scales formally with the third power. In contrast, the most accurate ab initio methods, CCSD(T), and G3, scale as the seventh power.…”

Effect of substituents on the stabilities of multiply-substituted carbon-centered radicals

“…This RB2-PLYP/6-311+G(3df,2p) procedure was found 9c, 22 to slightly (but consistently) underestimate the BDEs, giving a mean deviation of -6.9 kJ mol -1 and a mean absolute deviation of 6. 25 the HF and MP2 mixing parameters for the restricted-open-shell procedure were reoptimized, leading to a method referred to as ROB2-PLYP(59,28), indicating that it has 59% HF exchange and 28% MP2 correlation. As this procedure was found to show improved performance with regard to predicting RSEs, we decided to use it in this study (designating it simply as ROB2-PLYP from here onwards) in association with the 6-311+G(3df,2p) basis set 26 as the primary procedure for singlepoint energy calculations throughout the present study.…”

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

“…Table 1 gathers a summary of existing expression within this category [57][58][59][60][61][62][63][64][65][66][67][68]; broadly speaking, they differ in: (i) the kernel used to represent the exchange-correlation effects (i.e., B2-PLYP vs. mPW2-PLYP); (ii) the training set used to obtain the value of the {w EXX , w PT2 } weights, which is also related to the nature of the target set and the purpose of the parame- Table 1, it is readily seen how the weight of EXX is always considerably high, compared with the moderate weight for the perturbative term or with corresponding weight in hybrid models, and that a recently highlighted [69] condition such as w PT2 ≤ w EXX 2 , is almost invariably fulfilled independently of the final composition of these DH forms. These features are expected to largely drive the successful performance of the methods studied so far, as we will see next.…”