Semi-Empirical Born–Oppenheimer Molecular Dynamics (SEBOMD) within the Amber Biomolecular Package

Abstract

Semiempirical quantum methods from the Neglect of Differential Diatomic Overlap (NDDO) family such as MNDO, AM1, or PM3 are fast albeit approximate quantum methods. By combining them with linear scaling methods like the Divide & Conquer (D&C) method, it is possible to quickly evaluate the energy of systems containing hundreds to thousands of atoms. We here present our implementation in the Amber biomolecular package of a SEBOMD module that provides a way to run SemiEmpirical Born-Oppenheimer Molecular Dynamics. At each step of a SEBOMD molecular dynamics, a fully converged SCF calculation is performed to obtain the semiempirical quantum potential energy of a molecular system encaged or not in periodic boundary conditions. We describe the implementation and the features of our SEBOMD implementation. We show the requirements to conserve the total energy in NVE simulations, and how to accelerate SCF convergence through density matrix extrapolation. Specific ways of handling periodic boundary conditions using mechanical embedding or electrostatic embedding through a tailored quantum Ewald summation is developed. The parallel performance of SEBOMD simulations using the D&C scheme are presented for liquid water systems of various sizes, and a comparison between the traditional full diagonalization scheme and the D&C approach for the reproduction of the structure of liquid water illustrates the potentiality of SE-BOMD to simulate molecular systems containing several hundreds of atoms for hundreds of picoseconds with a quantum mechanical potential in a reasonable amount of CPU time.

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

“…Representative examples are discussed in section . For example, the latter utilizes either polynomial or Lagrange interpolation , of the charge densities obtained from the last several steps to estimate the effective initial guess at the current MD step. The coefficients for the linear combination of quantities to be extrapolated can also be generated via least-squares fitting of the consecutive geometries. , …”

ULYSSES: An Efficient and Easy to Use Semiempirical Library for C++

“…152 In this variant of the molecular dynamics technique, electrons are treated quantum mechanically, whereas the nuclei are allowed to move classically along the Born−Oppenheimer potential surface. 149 Two types of ensembles are currently available, NVE for which no thermostatting is required or NVT simulations using either the Berendsen thermostat 153 The SHAKE 155 and RATTLE algorithms 156 are available to constrain sets of bonds. These algorithms are typically very useful to keep reactions from happening during the equilibration stage.…”

“…ULYSSES is equipped with a dynamics class that allows Born–Oppenheimer Molecular Dynamics (BOMD) ,− using the leapfrog or the velocity Verlet algorithms . In this variant of the molecular dynamics technique, electrons are treated quantum mechanically, whereas the nuclei are allowed to move classically along the Born–Oppenheimer potential surface .…”

“…ULYSSES is equipped with a dynamics class that allows Born–Oppenheimer Molecular Dynamics (BOMD) ,− using the leapfrog or the velocity Verlet algorithms . In this variant of the molecular dynamics technique, electrons are treated quantum mechanically, whereas the nuclei are allowed to move classically along the Born–Oppenheimer potential surface . Two types of ensembles are currently available, NVE for which no thermostatting is required or NVT simulations using either the Berendsen thermostat or the Maxwell–Boltzmann scaling technique of Andrea et al…”

Dcdftbmd: Divide‐and‐Conquer Density Functional Tight‐Binding Program for Huge‐System Quantum Mechanical Molecular Dynamics Simulations

“…Combining approximate QM methods, semiempirical, tight‐binding (TB), and density functional TB (DFTB), to name a few with linear‐scaling methods is one of practical approaches to address the issue. The numerical tests and applications of linear‐scaling approximate QM methods have been reported over the last few decades …”