Three dimensional elongation method for large molecular calculations

Local electronic structure analysis by ab initio elongation method: A benchmark using DNA block polymers

The ab initio elongation (ELG) method based on a polymerization concept is a feasible way to perform linear-scaling electronic structure calculations for huge aperiodic molecules while maintaining computational accuracy. In the method, the electronic structures are sequentially elongated by repeating (1) the conversion of canonical molecular orbitals (CMOs) to region-localized MOs (RLMOs), that is, active RLMOs localized onto a region close to an attacking monomer or frozen RLMOs localized onto the remaining region, and the subsequent (2) partial self-consistent-field calculations for an interaction space composed of the active RLMOs and the attacking monomer. For each ELG process, one can obtain local CMOs for the interaction space and the corresponding local orbital energies. Local site information, such as the local highest-occupied/lowest-unoccupied MOs, can be acquired with linear-scaling efficiency by correctly including electronic effects from the frozen region. In this study, we performed a local electronic structure analysis using the ELG method for various DNA block polymers with different sequential patterns. This benchmark aimed to confirm the effectiveness of the method toward the efficient detection of a singular local electronic structure in unknown systems as a future practical application. We discussed the high-throughput efficiency of our method and proposed a strategy to detect singular electronic structures by combining with a machine learning technique.

Ab initio multi-level layered elongation method and its application to local interaction analysis between DNA bulge and ligand molecules

A multi-level layered elongation method was developed for efficiently analyzing the electronic states of local structures in large bio/nano-systems at the full ab initio level of theory. The original elongation method developed during the last three decades in our group has focused on the system in one direction from one terminal to the other terminal to sequentially construct the electronic states of a polymer, called a theoretical synthesis of polymers. In this study, an important region termed the central (C) part is targeted in a large polymer and the remainder are terminal (T) parts. The electronic structures along with polymer elongation are calculated repeatedly from both end T parts to the C central part at the same time. The important C part is treated with large basis sets (high level) and the other regions are treated with small basis sets (low level) in the ab initio theoretical framework. The electronic structures besides the C part can be reused for other systems with different structures at the C part, which renders the method computationally efficient. This multi-level layered elongation method was applied to the investigation on DNA single bulge recognition of small molecules (ligands). The reliability and validity of our approach were examined in comparison with the results obtained by direct calculations using a conventional quantum chemical method for the entire system. Furthermore, stabilization energies by the formation of the complex of bulge DNA and a ligand were estimated with basis set superposition error corrections incorporated into the elongation method.

Elongation method with intermediate mechanical and electrostatic embedding for geometry optimizations of polymers

The elongation method with intermediate mechanical and electrostatic embedding (ELG-IMEE) is proposed. The electrostatic embedding uses atomic charges generated by a charge sensitivity analysis (CSA) method and parameterized for three different population analyses, namely, the Merz-Singh-Kollman scheme, the charge model 5, and the atomic polar tensor. The obtained CSA models were tested on two model systems. Test calculations show that the electrostatic embedding provides several times of decrease in the difference of energies of testing and reference calculations in comparison with the conventional elongation approach (ELG). The mechanical embedding is implemented in a combination of the conventional elongation method and the ONIOM approach. Moreover, it was demonstrated that the geometry optimization with the ELG-IMEE reduces the errors in the optimized structures by about one order in root-mean-square deviation, when compared to ELG.

Intermediate electrostatic field for the generalized elongation method

An intermediate electrostatic field is introduced to improve the accuracy of fragment-based quantum-chemical computational methods by including long-range polarizations of biomolecules. The point charge distribution of the intermediate field is generated by a charge sensitivity analysis that is parameterized for five different population analyses, namely, atoms-in-molecules, Hirshfeld, Mulliken, natural orbital, and Voronoi population analysis. Two model systems are chosen to demonstrate the performance of the generalized elongation method (ELG) combined with the intermediate electrostatic field. The calculations are performed for the STO-3G, 6-31G, and 6-31G(d) basis sets and compared with reference Hartree-Fock calculations. It is shown that the error in the total energy is reduced by one order of magnitude, independently of the population analyses used. This demonstrates the importance of long-range polarization in electronic-structure calculations by fragmentation techniques.

Intermediate electrostatic field for the elongation method

A simple way to improve the accuracy of the fragmentation methods is proposed. The formalism was applied to the elongation (ELG) method at restricted open-shell Hartree-Fock (ROHF) level of theory. The α-helix conformer of polyglycine was taken as a model system. The modified ELG method includes a simplified electrostatic field resulting from point-charge distribution of the system's environment. In this way the long-distance polarization is approximately taken into account. The field attenuates during the ELG process to eventually disappear when the final structure is reached. The point-charge distributions for each ELG step are obtained from charge sensitivity analysis (CSA) in force-field atoms resolution. The presence of the intermediate field improves the accuracy of ELG calculations. The errors in total energy and its kinetic and potential contributions are reduced by at least one-order of magnitude. In addition the SCF convergence of ROHF scheme is improved.

An Efficient Local Molecular Dynamics Polymerization Simulation Combined with an Ab Initio MO Method

A new local ab initio molecular dynamics method, namely elongation molecular dynamics (ELG-MD) is proposed for highly efficient simulations of aperiodic polymer systems. ELG-MD combines the elongation method (ELG) with the Gear predictor corrector (GPC) algorithm of molecular dynamics simulation. In this method, the local gradients acting on the atom’s nucleus in the active region are calculated by the ELG method while the equations of the nucleus’s motion are solved by the GPC algorithm. In this work, the first application of this ELG-MD method is described to investigate the stable conformation of polyglycine with surrounding water molecules. The water effects on the structure of polyglycine are examined. The ELG-MD simulations show that the formation of the polyglycine helix is strongly induced by the hydrogen bonds observed in two types of H-bond rings.