Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion

Abstract

The balance between cost-effective and sufficiently accurate methods represents the proverbial "promised land" for quantum chemistry calculations. The burden thus falls upon theoretical and computational chemists to provide such alternatives to mitigate the issues that arise from the employ of finite computing resources. In this paper, we attempt to demonstrate the importance of the quality of the initial guess for the self-consistent field (SCF) calculation when considering cost reduction techniques. We broach this challenge by using the many body expansion (MBE) to yield high quality density matrices (DMs) which, in turn, are applied as an SCF initial guess. The MBE-DM approaches combined with purification schemes and distance-based cutoff schemes can serve as initial guesses to reduce the SCF cycles necessary for convergence or derive energy directly through one Fock build. To this end, four unique types of clusters including water clusters, fluoride anion water clusters, sodium cation water clusters, and ammonium-bisulfate salt clusters have been used to test the performance of MBE-DM where its truncation at three-body expansion, MBE(3)-DM, shows vast improvement for those four clusters with reductions in the number of SCF cycles up to 40% as compared with the traditional superposition of atomic densities (SAD) guess. Other types of typical initial guesses, superposition of atomic potentials (SAP) and basis set projection (BSP), perform much worse than MBE-DM and SAD. In addition, the MBE-DM shows consistency across an array of fragment types irrespective of charges, size, level of theory, and basis set selection. Through MBE(3)-DM with the distance cutoff and the average purification scheme, the energy can be obtained directly with a mere 3.2 mH of the mean absolute deviation (MAD) for (H 2 O) N=6−55 which is at least 73 times better than the energy prediction using the typical initial guesses (SAD, SAP, and BSP). The corresponding MAD per monomer is only 0.14 mH which reaches the threshold of the "dynamical accuracy". The promising results of the methods outlined in this paper not only indicate two direct routes for computational cost reduction but also lay the possible foundation for composite techniques (i.e., ab initio sampling) that make best use of near converged values as their starting point.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase

“…52,57,62,63,70,100,104,148,149 Alternatively, a many body expansion method to improve the SCF initial guess and, therefore, reduce the computational time was recently proposed. 105 The development of a robust scheme to converge higher excited states would be beneficial, especially since ΔSCF is a powerful method to track a specific state within the manifold of excited electronic states in a condensed phase system. 150 An interest in orbital-dependent functionals for exchange-correlation energies has been repeatedly expressed, but this has not yet gained traction in the ΔSCF research.…”

“…As mentioned above, the nature of the states has to be known upfront and their convergence depends on the quality of the initial guess. 105 Specification of fragment charges also proved to be necessary to predict the charge transfer state of a supersystem with large interfragment separation. 49 Optimization of excited state densities dissimilar from the ground state density is challenging.…”

Mapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians

“…It is known that the number of SCF cycles needed to reach convergence depends on the quality of the initial guess, P guess . 10 A good initial guess will require fewer SCF cycles, while a poor initial guess will require more SCF cycles or even worse lead to SCF convergence issues. [10][11][12][13] Exploring a potential energy surface (PES) is a commonly performed computational study in chemical research, where one has to do many SCF calculations along different molecular geometries for mapping out the surface.…”

“…10 A good initial guess will require fewer SCF cycles, while a poor initial guess will require more SCF cycles or even worse lead to SCF convergence issues. [10][11][12][13] Exploring a potential energy surface (PES) is a commonly performed computational study in chemical research, where one has to do many SCF calculations along different molecular geometries for mapping out the surface. One of the current practice is to use a sparse grid obtained from ab initio calculations to build a PES.…”

“…It is known that the number of SCF cycles needed to reach convergence depends on the quality of the initial guess, P guess . 10 A good initial guess will require fewer SCF cycles, while a poor initial guess will require more SCF cycles or even worse lead to SCF convergence issues. 10–13…”