Höfener Sebastian, Bischoff Florian A, Glöss Andreas, Klopper Wim
Center for Functional Nanostructures (CFN) and Lehrstuhl für Theoretische Chemie, Institut für Physikalische Chemie, Universität Karlsruhe (TH), D-76128, Karlsruhe, Germany.
Phys Chem Chem Phys. 2008 Jun 21;10(23):3390-9. doi: 10.1039/b803575j. Epub 2008 May 6.
In the recent years, Slater-type geminals (STGs) have been used with great success to expand the first-order wave function in an explicitly-correlated perturbation theory. The present work reports on this theory's implementation in the framework of the Turbomole suite of programs. A formalism is presented for evaluating all of the necessary molecular two-electron integrals by means of the Obara-Saika recurrence relations, which can be applied when the STG is expressed as a linear combination of a small number (n) of Gaussians (STG-nG geminal basis). In the Turbomole implementation of the theory, density fitting is employed and a complementary auxiliary basis set (CABS) is used for the resolution-of-the-identity (RI) approximation of explicitly-correlated theory. By virtue of this RI approximation, the calculation of molecular three- and four-electron integrals is avoided. An approximation is invoked to avoid the two-electron integrals over the commutator between the operators of kinetic energy and the STG. This approximation consists of computing commutators between matrices in place of operators. Integrals over commutators between operators would have occurred if the theory had been formulated and implemented as proposed originally. The new implementation in Turbomole was tested by performing a series of calculations on rotational conformers of the alkanols n-propanol through n-pentanol. Basis-set requirements concerning the orbital basis, the auxiliary basis set for density fitting and the CABS were investigated. Furthermore, various (constrained) optimizations of the amplitudes of the explicitly-correlated double excitations were studied. These amplitudes can be optimized in orbital-variant and orbital-invariant manners, or they can be kept fixed at the values governed by the rational generator approach, that is, by the electron cusp conditions. Electron-correlation effects beyond the level of second-order perturbation theory were accounted for by conventional coupled-cluster calculations with single, double and perturbative triple excitations [CCSD(T)]. The explicitly-correlated perturbation theory results were combined with CCSD(T) results and compared with literature data obtained by basis-set extrapolation.
近年来，斯莱特型双电子基函数（STG）在显式相关微扰理论中用于展开一阶波函数取得了巨大成功。本工作报道了该理论在Turbomole程序套件框架中的实现。提出了一种形式体系，通过小原-斋贺递推关系来计算所有必要的分子双电子积分，当STG表示为少量（n）高斯函数的线性组合（STG-nG双电子基）时该关系可适用。在该理论的Turbomole实现中，采用了密度拟合，并使用互补辅助基组（CABS）进行显式相关理论的单位分解（RI）近似。借助这种RI近似，避免了分子三电子和四电子积分的计算。引入了一种近似来避免动能算符与STG之间对易子的双电子积分。该近似包括计算矩阵之间的对易子以代替算符。如果按照最初提出的那样制定和实现该理论，就会出现算符之间对易子的积分。通过对正丙醇到正戊醇的链烷醇旋转构象进行一系列计算，对Turbomole中的新实现进行了测试。研究了关于轨道基、密度拟合辅助基组和CABS的基组要求。此外，还研究了显式相关双激发振幅的各种（约束）优化。这些振幅可以以轨道可变和轨道不变的方式进行优化，或者可以固定在由有理生成器方法（即电子尖点条件）确定的值上。二阶微扰理论水平以上的电子相关效应通过具有单、双和微扰三激发的传统耦合簇计算[CCSD(T)]来考虑。将显式相关微扰理论结果与CCSD(T)结果相结合，并与通过基组外推获得的文献数据进行比较。
