R12 methods in explicitly correlated molecular electronic structure theory
R12 methods in explicitly correlated molecular electronic structure theory
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显式关联分子电子结构理论中的 R12 方法
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Edward F. Valeev
中科院分区：
文献类型：
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作者：
W. Klopper;F. Manby;S. Ten;Edward F. Valeev
在过去的几年里，电子关联的明确关联的R12理论的发展经历了一个特别丰富的时期。这些理论绕过了传统方法的缓慢收敛，通过增加传统的轨道展开与少量的条款，明确取决于电子间距离r 12。在我们将在这里回顾的众多发现和发展中，有两个特别令人感兴趣。首先，R12方法的基本数值近似经受住了最严格的审查：Kutzelnigg使用恒等式的解析和广义布里渊条件来避免多电子积分仍然是合理的。第二，通过将对电子间坐标的依赖性从线性（r12）改变为某种适当选择的短程形式（例如，exp（− α r 12））。现代R12（或F12）方法可以提供MP2能量（及以上），这些能量在三重甚至双zeta基组中收敛到化学精度（1 kcal/mol）。使用一系列的近似，大分子的应用成为可能。在这里，在该领域的主要发展进行审查，并提出建议，为未来的发展方向。通过与常用的外推技术的比较，它表明，现代R12方法可以提供高精度显着快于使用传统的方法。目录PAGE 1.引言429 1.1.问题的起源429 1.2.双电子系统430 1.3.解释性相关MP2方法430 1.4.高斯双子431 1.5.指数相关高斯431 32 1.6.互相关方法433 2.R12波函数433 2.1.定义434 2.2.相关因子435 2.3.投影算子437 2.4.理论层次439 2.5.开壳方法439 40 3.多电子积分的近似441 3.1.精确求值442 3.2.近似：GBC，EBC和443 3.3.同一性的分辨率445 3.4.数值求积447 3.5.密度拟合449 3.6. DF与RI相结合451 4.第二个例子-4.1.技术细节453 4.2. R12结果与外推值的比较454 4.3. R12和F12结果的比较458 5.前景461 5.1.更高层次的方法461 5.2.@2.局部近似461 5.3.结论462 5.3.1.相关系数 5.3.2.投影算子462 5.3.3.中间体B 463的配制 5.3.4.近似积分463 5.3.5.提高效率
The past few years have seen a particularly rich period in the development of the explicitly correlated R12 theories of electron correlation. These theories bypass the slow convergence of conventional methods, by augmenting the traditional orbital expansions with a small number of terms that depend explicitly on the interelectronic distance r 12. Amongst the very numerous discoveries and developments that we will review here, two stand out as being of particular interest. First, the fundamental numerical approximations of the R12 methods withstand the closest scrutiny: Kutzelnigg's use of the resolution of the identity and the generalized Brillouin condition to avoid many-electronic integrals remains sound. Second, it transpires that great gains in accuracy can be made by changing the dependence on the interelectronic coordinate from linear (r 12) to some suitably chosen short-range form (e.g., exp(−αr 12)). Modern R12 (or F12) methods can deliver MP2 energies (and beyond) that are converged to chemical accuracy (1 kcal/mol) in triple- or even double-zeta basis sets. Using a range of approximations, applications to large molecules become possible. Here, the major developments in the field are reviewed, and recommendations for future directions are presented. By comparing with commonly used extrapolation techniques, it is shown that modern R12 methods can deliver high accuracy dramatically faster than by using conventional methods. Contents PAGE 1. Introduction 429 1.1. The origin of the problem 429 1.2. Two-electron systems 430 1.3. Explicitly correlated MP2 methods 430 1.4. Gaussian geminals 431 1.5. Exponentially correlated Gaussians 432 1.6. The transcorrelated method 433 2. R12 wavefunctions 433 2.1. Definition 434 2.2. Correlation factors 435 2.3. Projection operators 437 2.4. Levels of theory 439 2.5. Methods for open shells 440 3. Approximations of many-electron integrals 441 3.1. Exact evaluation 442 3.2. Approximations: GBC, EBC and 443 3.3. Resolution of the identity 445 3.4. Numerical quadrature 447 3.5. Density fitting 449 3.6. DF combined with RI 451 4. Examples from second-order perturbation theory 452 4.1. Technical details 453 4.2. R12 results in comparison with extrapolated values 454 4.3. Comparison between R12 and F12 results 458 5. Perspectives 461 5.1. Higher level methods 461 5.2. Local approximations 461 5.3. Conclusions 462 5.3.1. Correlation factor 462 5.3.2. Projection operator 462 5.3.3. Formulation of intermediate B 463 5.3.4. Approximating integrals 463 5.3.5. Efficiency improvements 463 Acknowledgements 463 References 464