A multi-center quadrature scheme for the molecular continuum
A multi-center quadrature scheme for the molecular continuum
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分子连续体的多中心求积方案
DOI：
10.1016/j.cpc.2021.107889
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发表时间：
2021
影响因子：
6.3
通讯作者：
Argenti, L.
中科院分区：
文献类型：
--
作者：
Gharibnejad, H.;Douguet, N.;Schneider, B.I.;Olsen, J.;Argenti, L.
计算多原子分子电子积分的一种常见方法是使用Becke的配分方案(Becke and Chem，1988)和以每个原子位为中心的重叠格子。Becke方案是为长距离快速脱落的积分体设计的，例如那些近似束缚电子态的积分体。然而，当应用于电子连续体中的态时，Becke格式表现出缓慢的收敛速度和高度的冗余性。在这里，我们提出了一种改进的Becke方案，它适用于电子连续统的函数，如分子光电离和电子-分子散射，并确保了收敛和效率与在计算束缚态时所实现的相当。在这个改进的方案中，已经存在于Becke分区中的原子量在它们各自的原子核的几个键长范围内被平滑地切断，并由一个渐近么正重量补充。原子积分是在以每个原子为中心的小球面网格上计算的，其大小与相应原子量的支承相称。用中心主网格计算间隙区域和长程区域的剩余积分。通过计算原子格点上含有Gauss型轨道和Yukawa势的被积函数以及以主网格为中心的球面Bessel函数，验证了该方法的准确性。这些函数代表了在实际的多原子分子的电子散射和光电离计算中遇到的那些函数。
A common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 1988) in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron–molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.
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量子计算：精度累加、展开函数不受限制、计算经济
DOI：
--
发表时间：
1966
期刊：
影响因子：
--
作者：
S. F. Boys;P. Rajagopal
通讯作者：
P. Rajagopal
DOI：
10.1088/0953-4075/22/14/007
发表时间：
1989-07-28
影响因子：
1.6
作者：
KAUFMANN, K;BAUMEISTER, W;JUNGEN, M
通讯作者：
JUNGEN, M
DOI：
--
发表时间：
1988
期刊：
影响因子：
--
作者：
P. Boerrigter;G. T. Velde;J. E. Baerends
通讯作者：
J. E. Baerends
DOI：
--
发表时间：
1967
期刊：
影响因子：
--
作者：
D. M. Bishop
通讯作者：
D. M. Bishop
DOI：
--
发表时间：
1989
期刊：
Physical Review B (Condensed Matter)
影响因子：
--
作者：
Averill;Painter
通讯作者：
Painter