Molecular Tailoring: An Art of the Possible for Ab Initio Treatment of Large Molecules and Molecular Clusters

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Vibrational infrared and Raman spectra of polypeptides: Fragments-in-fragments within molecular tailoring approach

The present work reports the calculation of vibrational infrared (IR) and Raman spectra of large molecular systems employing molecular tailoring approach (MTA). Further, it extends the grafting procedure for the accurate evaluation of IR and Raman spectra of large molecular systems, employing a new methodology termed as Fragments-in-Fragments (FIF), within MTA. Unlike the previous MTA-based studies, the accurate estimation of the requisite molecular properties is achieved without performing any full calculations (FC). The basic idea of the grafting procedure is implemented by invoking the nearly basis-set-independent nature of the MTA-based error vis-à-vis the respective FCs. FIF has been tested out for the estimation of the above molecular properties for three isomers, viz., β-strand, 310- and α-helix of acetyl(alanine)nNH2 (n = 10, 15) polypeptides, three conformers of doubly protonated gramicidin S decapeptide and trpzip2 protein (PDB id: 1LE1), respectively, employing BP86/TZVP, M06/6-311G**, and M05-2X/6-31G** levels of theory. For most of the cases, a maximum difference of 3 cm(-1) is achieved between the grafted-MTA frequencies and the corresponding FC values. Further, a comparison of the BP86/TZVP level IR and Raman spectra of α-helical (alanine)20 and its N-deuterated derivative shows an excellent agreement with the existing experimental spectra. In view of the requirement of only MTA-based calculations and the ability of FIF to work at any level of theory, the current methodology provides a cost-effective solution for obtaining accurate spectra of large molecular systems.

Low energy isomers of (H2O)25 from a hierarchical method based on Monte Carlo temperature basin paving and molecular tailoring approaches benchmarked by MP2 calculations

We report new global minimum candidate structures for the (H2O)25 cluster that are lower in energy than the ones reported previously and correspond to hydrogen bonded networks with 42 hydrogen bonds and an interior, fully coordinated water molecule. These were obtained as a result of a hierarchical approach based on initial Monte Carlo Temperature Basin Paving sampling of the cluster's Potential Energy Surface with the Effective Fragment Potential, subsequent geometry optimization using the Molecular Tailoring Approach with the fragments treated at the second order Møller-Plesset (MP2) perturbation (MTA-MP2) and final refinement of the entire cluster at the MP2 level of theory. The MTA-MP2 optimized cluster geometries, constructed from the fragments, were found to be within <0.5 kcal/mol from the minimum geometries obtained from the MP2 optimization of the entire (H2O)25 cluster. In addition, the grafting of the MTA-MP2 energies yields electronic energies that are within <0.3 kcal/mol from the MP2 energies of the entire cluster while preserving their energy rank order. Finally, the MTA-MP2 approach was found to reproduce the MP2 harmonic vibrational frequencies, constructed from the fragments, quite accurately when compared to the MP2 ones of the entire cluster in both the HOH bending and the OH stretching regions of the spectra.

Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 2. Level of Theory, Basis Set, and Solvents Model Dependence

It has been demonstrated that the fragmentation scheme of our adjustable density matrix assembler (ADMA) approach for the quantum chemical calculations of very large systems is well-suited to calculate NMR chemical shifts of proteins [ Frank et al. Proteins2011, 79, 2189-2202 ]. The systematic investigation performed here on the influences of the level of theory, basis set size, inclusion or exclusion of an implicit solvent model, and the use of partial charges to describe additional parts of the macromolecule on the accuracy of NMR chemical shifts demonstrates that using a valence triple-ζ basis set leads to large improvement compared to the results given in the previous publication. Additionally, moving from the B3LYP to the mPW1PW91 density functional and including partial charges and implicit solvents gave the best results with mean absolute errors of 0.44 ppm for hydrogen atoms excluding H(N) atoms and between 1.53 and 3.44 ppm for carbon atoms depending on the size and also on the accuracy of the protein structure. Polar hydrogen and nitrogen atoms are more difficult to predict. For the first, explicit hydrogen bonds to the solvents need to be included and, for the latter, going beyond DFT to post-Hartree-Fock methods like MP2 is probably required. Even if empirical methods like SHIFTX+ show similar performance, our calculations give for the first time very reliable chemical shifts that can also be used for complexes of proteins with small-molecule ligands or DNA/RNA. Therefore, taking advantage of its ab initio nature, our approach opens new fields of application that would otherwise be largely inaccessible due to insufficient availability of data for empirical parametrization.