Bakowies Dirk
Laboratory of Physical Chemistry, ETH Zürich, CH 8093 Zürich, Switzerland.
J Chem Phys. 2007 Oct 28;127(16):164109. doi: 10.1063/1.2768359.
A new two-point scheme is proposed for the extrapolation of electron correlation energies obtained with small basis sets. Using the series of correlation-consistent polarized valence basis sets, cc-pVXZ, the basis set truncation error is expressed as deltaE(X) proportional, variant(X + xi(i))(-gamma). The angular momentum offset xi(i) captures differences in effective rates of convergence previously observed for first-row molecules. It is based on simple electron counts and tends to values close to 0 for hydrogen-rich compounds and values closer to 1 for pure first-row compounds containing several electronegative atoms. The formula is motivated theoretically by the structure of correlation-consistent basis sets which include basis functions up to angular momentum L = X-1 for hydrogen and helium and up to L = X for first-row atoms. It contains three parameters which are calibrated against a large set of 105 reference molecules (H, C, N, O, F) for extrapolations of MP2 and CCSD valence-shell correlation energies from double- and triple-zeta (DT) and triple- and quadruple-zeta (TQ) basis sets. The new model is shown to be three to five times more accurate than previous two-point schemes using a single parameter, and (TQ) extrapolations are found to reproduce a small set of available R12 reference data better than even (56) extrapolations using the conventional asymptotic limit formula deltaE(X) proportional, variantX(-3). Applications to a small selection of boron compounds and to neon show very satisfactory results as well. Limitations of the model are discussed.
本文提出了一种新的两点外推方案，用于由小基组获得的电子相关能的外推。使用一系列相关一致的极化价基组cc-pVXZ，基组截断误差表示为$\Delta E(X)\propto(X+\xi(i))^{-\gamma}$。角动量偏移量$\xi(i)$反映了先前在第一行分子中观察到的有效收敛速率的差异。它基于简单的电子计数，对于富氢化合物，其值趋于接近0，而对于含有多个电负性原子的纯第一行化合物，其值更接近1。该公式在理论上由相关一致基组的结构推导得出，对于氢和氦，相关一致基组包含角动量高达$L = X - 1$的基函数，对于第一行原子，角动量高达$L = X$。该公式包含三个参数，通过对105个参考分子（H、C、N、O、F）的大量数据集进行校准，用于从双ζ和三ζ（DT）以及三ζ和四ζ（TQ）基组外推MP2和CCSD价层相关能。新模型的准确性比使用单个参数的先前两点方案高三到五倍，并且发现（TQ）外推比使用传统渐近极限公式$\Delta E(X)\propto X^{-3}$的（56）外推能更好地重现一小部分可用的R12参考数据。对一小部分硼化合物和氖的应用也显示出非常令人满意的结果。本文还讨论了该模型的局限性。
