Accelerating molecular property calculations with semiempirical preconditioning.

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Quantum Chemistry

Background:

• Ab initio calculations of molecular properties involve solving large-scale eigenvalue problems.
• Krylov space algorithms, like the Davidson algorithm, are commonly used for these computations.
• Preconditioners are essential for optimizing iterative Krylov space algorithms.

Purpose of the Study:

• To accelerate ab initio calculations of molecular linear response properties.
• To improve the efficiency of iterative solvers by enhancing preconditioners.
• To combine the speed of semiempirical methods with the accuracy of ab initio methods.

Main Methods:

• Utilizing semiempirical approximations as preconditioners within Krylov space algorithms.
• Applying the simplified time-dependent density functional theory (TD-DFT) semiempirical model.
• Accelerating calculations for electronic excitation energies and electric polarizabilities.

Main Results:

• The semiempirical preconditioner reduced iterations for excitation energies by an average of 37% (up to 70%).
• Iterations for polarizability calculations decreased by an average of 15% (up to 33%).
• Tuning empirical parameters in the semiempirical model yielded an additional ~20% reduction in iterations.

Conclusions:

• Semiempirical preconditioners significantly accelerate ab initio property calculations.
• This approach offers a speedup without compromising the accuracy of the converged results.
• The method provides a pathway to integrate the efficiency of semiempirical models with the precision of ab initio techniques.