Iterative Solvers for Empirical Partial Atomic Charges: Breaking the Curse of Cubic Numerical Complexity

Area of Science:

• Computational chemistry
• Molecular modeling
• Drug design

Background:

• Rational drug design relies on accurate electrostatic interaction modeling using atomic charges.
• Computational inefficiency in these calculations hinders method development and dissemination.
• Solving systems of linear algebraic equations (SLAE) is central to empirical atomic charge calculation methods.

Purpose of the Study:

• To investigate the application of iterative methods for solving SLAE in empirical atomic charge calculations.
• To demonstrate how iterative solvers can reduce computational complexity and speed up calculations.
• To explore the potential of these optimized methods for broader applications in computational chemistry.

Main Methods:

• Solving systems of linear algebraic equations (SLAE) using iterative methods.
• Comparing the computational complexity of iterative solvers (quadratic) with classical methods like Gauss elimination (cubic).
• Analyzing the properties of matrices arising from empirical atomic charge calculations to assess suitability for iterative solvers.

Main Results:

• Iterative methods reduce computational complexity for atomic charge calculations from cubic to near-quadratic.
• Empirical schemes yield SLAE matrices well-suited for efficient iterative solvers.
• This approach offers a significant speed-up compared to non-iterative solvers.

Conclusions:

• The systematic application of iterative solvers to empirical atomic charge calculations offers substantial computational benefits.
• Optimized atomic charge calculations can enhance the feasibility of complex simulations, such as molecular dynamics with polarizability.
• This work promotes wider adoption of efficient computational techniques in rational drug design.