A combined first- and second-order optimization method for improving convergence of Hartree–Fock and Kohn–Sham calculations

Kreplin, David A.; Werner, Hans‐Joachim

doi:10.1063/5.0094292

Cited by 4 publications

(4 citation statements)

References 56 publications

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“…More recently, a number of variations of the DIIS method have been suggested. − The augmented Roothaan–Hall approach is an alternative approach, sometimes used in conjunction with the DIIS approach. − A number of restricted-step second-order methods have also been presented and implemented. − Alternatively, new hybrid methods have been devised to utilize the pros of second-order methods and the DIIS approach. , Overall, these methods generally provide satisfactory convergence statistics. However, as the electronic structure of the target molecule starts to exhibit near-degeneracy effects and open-shell characteristics, it is not uncommon to experience poor convergence or no convergence at all.…”

Section: Introductionmentioning

confidence: 99%

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A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

Sethio,

Azzopardi,

Fdez. Galván

et al. 2024

J. Phys. Chem. A

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In this work, three versions of self-consistent field/ Kohn−Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/ RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small-to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed-and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

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Section: Introductionmentioning

confidence: 99%

“… 15 − 19 A number of restricted-step second-order methods have also been presented and implemented. 20 − 25 Alternatively, new hybrid methods have been devised to utilize the pros of second-order methods and the DIIS approach. 26 , 27 Overall, these methods generally provide satisfactory convergence statistics.…”

Section: Introductionmentioning

confidence: 99%

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

Sethio,

Azzopardi,

Fdez. Galván

et al. 2024

J. Phys. Chem. A

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show abstract

“…The augmented Roothaan-Hall approach is an alternative approach, sometimes used in conjunction with the DIIS approach [15][16][17][18][19] . A number of restricted-step second-order methods have also been presented and implemented [20][21][22][23][24][25] . Alternatively, new hybrid methods have been devised to utilize the pros of second order methods and the DIIS approach 26,27 .…”

Section: Introductionmentioning

confidence: 99%

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

Sethio,

Azzopardi,

Fernández Galván

et al. 2024

Preprint

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In this report, three versions of SCF/KS-DFT orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient enhanced Kriging method, combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed to improve the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine technique that has proved successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to standard state-of-the-art SCF/KS-DFT optimization methods.

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“…The augmented Roothaan-Hall approach is an alternative approach, sometimes used in conjunction with the DIIS approach [16][17][18][19][20] . A number of restricted-step second-order methods have also been presented and implemented [21][22][23][24][25][26] . Alternatively, new hybrid methods have been devised to utilize the pros of second order methods and the DIIS approach 27,28 .…”

Section: Introductionmentioning

confidence: 99%

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

Sethio,

Azzopardi,

Fernández Galván

et al. 2023

Preprint

View full text Add to dashboard Cite

In this report, three versions of SCF/KS-DFT orbital optimization are described and benchmarked. The methods are a modified version of the gradient type of the direct inversion in the iterative subspace approach (r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient enhanced Kriging method, combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed to improve the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine technique that has proved successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to standard state-of-the-art SCF/KS-DFT optimization methods.

show abstract

A combined first- and second-order optimization method for improving convergence of Hartree–Fock and Kohn–Sham calculations

Cited by 4 publications

References 56 publications

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

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