Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method

Neese, Frank; Wennmohs, Frank; Hansen, Andreas

doi:doi:10.1063/1.3086717

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A study of the fixed-node error in quantum Monte Carlo calculations of electronic transitions: The case of the singlet n→π^∗ (CO) transition of the acrolein

We report fixed-node diffusion Monte Carlo (FN-DMC) calculations of the singlet n→π∗ (CO) vertical transition of acrolein. The impact of the fixed-node approximation on the excitation energy is investigated. To do that, trial wave functions corresponding to various nodal patterns are used. They are constructed by using either a minimal complete-active-space self-consistent field (CASSCF) calculation involving an oxygen lone pair n and the π∗ (CO) molecular orbitals or a more complete set involv...

Hydrogen multicenter bonds and reversible hydrogen storage

A new strategy for reversible hydrogen storage based on the properties of hydrogen multicenter bonds is proposed. This is demonstrated by carrying out ab initio calculations of hydrogen saturation of titanium and bimetallic titanium-aluminum nanoclusters. Hydrogen saturation leads to the formation of exceptionally and energetically stable hydrogen multicenter bonds. The stabilization results from sharing of the hydrogen atom electron density with the frontier orbitals of the metal cluster. The ...

Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Møller–Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50–100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol⁻¹. Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chemical applications.

Article Outline

INTRODUCTION
THEORY
1. The closed-shell CISD and CEPA equations
2. PNOs
3. Improved PNOs
4. PNO form of the residual
5. Approximations
6. Perturbative correction
7. Implementation
NUMERICAL RESULTS
1. Computational details
2. Accuracy
  1. Dependence of the results on the thresholds
  2. PNO distributions
  3. Dependence of the results on the localization method
  4. Dependence of the results on the PNO construction method
  5. Study of the numerical error
  6. Reaction energies
  7. Weak interactions
3. Efficiency
  1. Scaling
  2. Analysis of timings
4. Smoothness of potential energy surfaces
  1. Bond dissociation: Ketene
  2. Rotational barriers
SUMMARY AND DISCUSSION

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KEYWORDS and PACS

Keywords

coupled cluster calculations, density functional theory, molecular configurations, orbital calculations, perturbation theory, potential energy surfaces, thermochemistry

PACS

31.15.E-

Density-functional theory
31.15.bw

Coupled-cluster theory
82.60.-s

Chemical thermodynamics
31.50.-x

Potential energy surfaces
33.15.Bh

General molecular conformation and symmetry; stereochemistry

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http://link.aip.org/link/doi/10.1063/1.3086717

PUBLICATION DATA

ISSN:

0021-9606 (print)

1089-7690 (online)

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American Institute of Physics

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