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Local and canonical approximations in Moller-Plesset perturbation theory with applications to dispersion interactions.

机译：Moller-Plesset微扰理论中的局部和规范近似及其在色散相互作用中的应用。

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摘要

The central theme of this thesis is the synergy between theoretical method development, efficient computational implementation, and relevant chemical application of second-order Moller-Plesset perturbation (MP2) theory. The central approximation utilized throughout this work involves the resolution-of-the-identity (RI) linear expansion of atomic orbital (AO) products in terms of an atom-centered auxiliary basis, thereby offering significant reductions in the computational effort necessary during AO integral evaluation and subsequent transformation into the molecular orbital (MO) basis. The primary chemical applications in this work center around dispersion interactions the ubiquitous, non-bonded intra- and inter-molecular interactions that play a key role in the stability and formation of protein secondary structure, base-pair stacking in the DNA double helix, dimer formation among rare gases, and other long-range correlation effects.;By incorporating the RI-approximation into the theoretical framework of the local triatomics-in-molecules (TRIM) model, we were able to simultaneously reduce the computational prefactor, via the RI-approximation for integral transformations from the AO to MO basis, and the inherent scaling of canonical MP2 theory, via the TRIM ansatz for local electron correlation, in which only double excitations that involve up to three atomic centers are retained. The resulting methodology, RI-TRIM MP2, emerged as a robust fourth-order method with the ability to extend the regime of practical MP2 calculations and to allow for treatment of electron correlation in molecular systems containing hundreds of atoms on a single processor.;An efficient serial implementation of the RI-MP2 analytical gradient utilizing a semi-direct t-amplitude batching approach was also presented and thoroughly assessed in terms of computational performance and chemical accuracy. As an application of this analytical RI-MP2 nuclear gradient algorithm, the structures and energetics characterizing the extended and globular conformations of alanine tetrapeptide were investigated with a focus on the role of dispersion interactions in the stability of folded conformational isomers of small polypeptide sequences.;Further exploration of analytical MP2 gradient theory was pursued in the development of the analytical gradient of RI-MP2 theory within the dual-basis (DB) approximation (DB-RI-MP2). By achieving self-consistent field (SCF) convergence in a small basis, projecting the small basis density into a target basis, and then approximating a single Roothaan step in the target basis via diagonalization of the Fock matrix built from the projected density, the DB formalism captures the linear energetic response to changes in the density matrix. In doing so, the DB model provides a fast and accurate route to obtaining the reference Hartree-Fock (HF) wavefunction, upon which MP2 corrections can be applied to account for dynamical electron correlation. A detailed analysis of the computational efficiency and chemical accuracy of the DB-RI-MP2 analytical gradient was presented herein and the significant changes to both the theory and computation of the coupled-perturbed self-consistent field equations (CPSCF) were explored. It was found that the simultaneous use of the DB- and RI-approximations not only provided highly-accurate MP2 analytical forces, but also directly targeted the computationally intensive underlying SCF-related steps necessary during analytical force determinations at the RI-MP2 level of theory, thereby allowing routine exploration of medium-sized molecular systems with large AO basis sets at the MP2 level of theory.;On the chemical application front, the spin-component scaled MP2 model (SCSMP2), in which the same and opposite spin contributions of the MP2 correlation energy are differentially scaled, was specialized to deal with Molecular Interactions by reoptimizing both spin-component scaling parameters on a diverse set of non-bonded complexes. The resultant model, SCS(MI)-MP2, emerged as a highly accurate methodology for obtaining intermolecular binding energies among both hydrogen-bonded and dispersion complexes with no additional cost over the underlying MP2 computation. An in-depth chemical application at the RI-MP2 level of theory followed that focused on the gas-phase benzene dimer, a primarily dispersion-bound molecular complex that serves as the prototype for pi-pi stacking in double-stranded DNA. A comparative analysis of the structure and energetics of the benzene dimer revealed the existence of two distorted dimeric binding motifs---configurations that represent the lowest energy T-shaped benzene dimer structures reported to date. (Abstract shortened by UMI.)
机译：本文的中心主题是理论方法开发，有效的计算实现以及二阶Moller-Plesset摄动（MP2）理论的相关化学应用之间的协同作用。在整个工作中使用的中心近似方法涉及以原子为中心的辅助基础的原子轨道（AO）乘积的分辨度（RI）线性扩展，从而显着减少了AO积分期间所需的计算量评估并随后转化为分子轨道（MO）。在这项工作中的主要化学应用围绕分散相互作用，普遍存在的，非键合的分子内和分子间相互作用，这些相互作用在蛋白质二级结构的稳定性和形成，DNA双螺旋中碱基对堆积，二聚体的形成中起着关键作用。通过将RI逼近合并到局部三分子模型（TRIM）模型的理论框架中，我们能够通过RI同时减少计算因子-从AO到MO的积分转换的近似，以及通过TRIM ansatz进行局部电子相关的规范MP2理论的固有缩放比例，其中仅保留涉及三个原子中心的双激发。最终的方法RI-TRIM MP2成为一种强大的四阶方法，能够扩展实际MP2计算范围，并允许在单个处理器上处理包含数百个原子的分子系统中的电子相关性。还提出了使用半直接t振幅分批方法对RI-MP2分析梯度进行有效的串行实施，并在计算性能和化学准确性方面进行了全面评估。作为这种分析性RI-MP2核梯度算法的应用，研究了表征丙氨酸四肽的扩展和球形构象的结构和能量学，重点研究了分散相互作用在小多肽序列折叠构象异构体稳定性中的作用。在双基（DB）逼近（DB-RI-MP2）内RI-MP2理论的分析梯度的发展中，对分析MP2梯度理论进行了进一步的探索。通过在较小的基础上实现自洽场（SCF）收敛，将较小的基础密度投影到目标基础，然后通过根据投影密度构建的Fock矩阵的对角化，在目标基础上近似单个Roothaan步长形式主义捕捉对密度矩阵变化的线性能量响应。通过这样做，DB模型为获得参考Hartree-Fock（HF）波函数提供了一种快速而准确的途径，可以在其上应用MP2校正来解决动态电子相关性。本文对DB-RI-MP2解析梯度的计算效率和化学准确性进行了详细分析，并探讨了耦合摄动自洽场方程（CPSCF）的理论和计算方面的重大变化。发现同时使用DB和RI近似不仅提供了高精度的MP2分析力，而且还直接针对了RI-MP2理论水平的分析力确定过程中所需的计算密集型基础SCF相关步骤。 ，从而可以在MP2的理论水平上常规研究具有大AO基集的中型分子系统。在化学应用方面，自旋组分缩放的MP2模型（SCSMP2），其中自旋贡献相同和相反MP2相关能量被差分缩放，专门用于通过优化一组非键合复合物上的两个自旋组分缩放参数来处理分子相互作用。由此产生的模型SCS（MI）-MP2成为获得氢键键合和分散配合物之间分子间结合能的高度精确的方法，而没有比基础MP2计算额外的成本。随后在理论上在RI-MP2级别上进行了深入的化学应用，重点是气相苯二聚体，该分子主要是与分散体结合的分子复合物，是pi-pi在双链DNA中堆叠的原型。对苯二聚体的结构和能量进行比较分析，发现存在两个扭曲的二聚体结合基序---构型，代表了迄今为止报道的最低能量的T形苯二聚体结构。 （摘要由UMI缩短。）

著录项

  • 作者

    DiStasio, Robert Anthony, Jr.;

  • 作者单位

    University of California, Berkeley.;

  • 授予单位 University of California, Berkeley.;
  • 学科 Chemistry Physical.;Physics Molecular.;Physics Theory.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 296 p.
  • 总页数 296
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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