Energy-based Fragmentation Method Research Articles

Accurate and efficient prediction of vibrational circular dichroism spectra of condensed-phase systems with the generalized energy-based fragmentation method

The vibrational circular dichroism (VCD) spectra could determine the molecular chirality of condensed-phase systems, but their quantum chemistry calculations are costly. The fragment-based methods have not been applied to the VCD spectra of periodic systems yet. In this work, we have extended the generalized energy-based fragmentation (GEBF) approach to accurately and efficiently compute the VCD spectra of chiral molecular crystals under periodic boundary conditions (PBCs) and macromolecules in solutions. In this approach, the Hessian matrices, atomic polar/axial tensors of a target system, are evaluated as a linear combination of the corresponding quantities from a series of small electrostatically embedded subsystems. Comparisons of GEBF and conventional VCD spectra of two large molecules show that this approach can satisfactorily reproduce the conventional computational results. Then, we applied the PBC-GEBF method to calculate the VCD spectra of a chiral molecular crystal and two macromolecules in solutions. Our results show that the experimental VCD spectrum can be roughly reproduced in terms of both band shape and vibrational peaks. The GEBF-VCD and PBC-GEBF-VCD approaches are expected to be practical tools to investigate the chirality of molecular crystals and macromolecules in solutions.

Structures and properties of ionic crystals and condensed phase ionic liquids predicted with the generalized energy-based fragmentation method.

The generalized energy-based fragmentation (GEBF) approach is extended to facilitate ab initio investigations of structures, lattice energies, vibrational spectra and 1 H NMR chemical shifts of ionic crystals and condensed-phase ionic liquids (ILs) with the periodic boundary conditions (PBC). For selected periodic systems, our results demonstrate that the so-called PBC-GEBF approach can provide satisfactory descriptions on ground-state energies, structures, and vibrational spectra of ionic crystals and IL crystals. The PBC-GEBF approach is then applied to three realistic condensed phase systems. For three ionic crystals (LiCl, NaCl, and KCl), we apply the PBC-GEBF approach with MP2 theory as well as some popular DFT methods to investigate their crystal structures and lattice energies. Our calculations indicate that the crystal structures obtained with PBC-GEBF-MP2/6-311 + G** are very close to the corresponding X-ray structures, while PBC-GEBF-ωB97X-D/6-311 + G** provides satisfactory prediction for crystal structures and lattice energies. For two polymorphs of [n-C4 mim][Cl] crystals, we find that the PBC-GEBF approach at the M06-2X/6-311 + G** level can give a satisfactory descriptions on structures and Raman spectra of these two crystals. Furthermore, for [C2 mim][BF4 ] ILs, we demonstrate that their 1 H NMR chemical shifts can be estimated from averaging over 5 typical snapshots (extracted from MD simulations) with the PBC-GEBF approach at the B97-2/pcSseg-2 level. The calculated results account for the observed experimental data quite well. Therefore, we expect that the PBC-GEBF approach, combined with various quantum chemistry methods, will become an effective tool in predicting structures and properties of ionic crystals and condensed-phase ILs.

Accurate and Efficient Prediction of NMR Parameters of Condensed-Phase Systems with the Generalized Energy-Based Fragmentation Method.

We have implemented the calculations of NMR parameters within the generalized energy-based fragmentation (GEBF) method for condensed-phase systems with periodic boundary conditions (PBC). In this PBC-GEBF approach, NMR parameters of molecules in a unit cell are assembled as a linear combination of the corresponding quantities from a series of small embedded subsystems. To treat condensed-phase systems containing large molecules, we propose a novel "fragment-based" strategy for building subsystems, while our previously reported "molecule-based" strategy for construction of subsystems is appropriate for periodic systems with small molecules. The "fragment-based" strategy in PBC-GEBF is demonstrated to be much more efficient than its "molecule-based" counterpart to treat crystals of large molecules. With the "molecule-based" PBC-GEBF method, we obtained consistently good NMR parameters of liquid water with B3LYP on top of neural-network-potential-based ab initio molecular dynamics (AIMD) snapshots. With the "fragment-based" PBC-GEBF approach, we predicted the 1H chemical shifts of a large macrocycle in solution based on a series of classical MD snapshots. The calculated results are in good accord with the experimental chemical shifts. Therefore, the PBC-GEBF method is expected to be a reliable and efficient tool for predicting NMR parameters of large complex systems in solutions.

Utilization of generalized energy-based fragmentation method on the study of hydrogen abstraction reactions of large methyl esters

Accurate reaction energies and barrier heights are essential for the construction of reliable combustion kinetics models of various fuels. Nevertheless, the computational cost for electronic energy calculations using high-level ab initio methods increases dramatically with the size of molecules. A solution to this problem is to utilize a generalized energy-based fragmentation (GEBF) approach, as it has been found to be effective in reducing the scaling of the computational cost in calculation of energetics and other molecular properties for many large molecules, clusters, and crystals with various quantum chemistry methods. This work attempts to apply this GEBF approach in the study of one important type of reactions of large methyl esters, i.e., the hydrogen abstraction reactions by hydrogen atoms. The energies of stationary points on the potential energy surfaces were examined using both conventional quantum chemistry methods and the GEBF method at the QCISD(T)/CBS// M06-2X/6-311 + + g(d,p) level for CnH2n+1COOCH3 (n = 4, 5) + H reactions. The results show that the unsigned energy deviation of the GEBF method from the conventional method is less than 0.1 kcal/mol, while the computational time is greatly reduced, e.g. up to 90% at the QCISD(T)/cc-pVTZ level. Based on the quantum chemistry calculations, rate constants of the hydrogen abstraction reactions of CnH2n+1COOCH3 (n = 4, 5, 8) by H atoms were computed.

Structures and properties of large supramolecular coordination complexes predicted with the generalized energy-based fragmentation method.

The generalized energy-based fragmentation (GEBF) method has been extended to facilitate ab initio calculations of large supramolecular coordination complexes. For metal-containing coordination complexes, a special fragmentation scheme is proposed for GEBF calculations, in which coordinate bonds between metal ions and ligands are kept intact, and only single covalent bonds in organic ligands are cut into fragments. A simple strategy is exploited for the determination of the ground-state spin multiplicity of each metal ion so that the total spin of all metal-containing subsystems is assigned automatically. With this fragmentation scheme, the GEBF method is demonstrated to provide reliable energies, optimized geometry, nuclear magnetic resonance (NMR) properties and the infrared spectrum for a medium-sized supramolecular coordination complex, which are very consistent with those from the full-system quantum chemistry calculations. The GEBF method is then applied to two large supramolecular coordination complexes to illustrate its capability. For the trimetallic coordination complex Fe2Zn2(RuL2)2 (with 618 atoms), the calculated 1H chemical shifts from GEBF calculations with the B97-2 functional can account well for the experimental NMR spectrum. For the cage-guest complex Pd4L8(BF4-)3, the computed infrared spectrum obtained with the GEBF-M06-2X method can help assign the experimental peaks to the corresponding vibrational motions. The GEBF method combining with advanced electronic structure methods is expected to be a useful tool to understand and interpret structural and spectroscopic information of various supramolecular coordination complexes.

Accurate Prediction of NMR Chemical Shifts in Macromolecular and Condensed-Phase Systems with the Generalized Energy-Based Fragmentation Method.

The generalized energy-based fragmentation (GEBF) method is extended to allow calculations of nuclear magnetic resonance (NMR) chemical shifts of macromolecular and condensed-phase systems feasible at a low computational cost. In this approach, NMR shielding constants in a large system are evaluated as a linear combination of the corresponding quantities from a series of small "electrostatically embedded" subsystems. Comparison of NMR shielding constants from the GEBF-X method [where X is an electronic structure method, such as Hartree-Fock (HF), density functional theory (DFT), ...] with those from the conventional quantum chemistry method for two representative systems verifies that the GEBF approach can reproduce the results of the conventional quantum chemistry method very well. This procedure has further been applied to compute NMR shielding constants of a large foldamer and a supramolecular aggregate, and the 15N shielding constant for CH3CN in the CHCl3 solvent. For the former two systems, the predicted 1H chemical shifts are in good agreement with the experimental data. For the CH3CN/CHCl3 solution, the 15N shielding constant of CH3CN is evaluated as the ensemble average of up to 200 sufficiently large CH3CN/CHCl3 clusters from either classical or QM/MM (quantum mechanics/molecular mechanics) molecular dynamics (MD) simulations. Our results reveal that the gas-to-solution shift of 15N (from an isolated CH3CN to the CH3CN/CHCl3 solution) based on PM6-DH+/MM MD simulation is in good accord with the experimental value, outperforming those based on classical MD simulation and the previous polarizable continuum model using integral equation formalism (IEF-PCM) study. This study unravels that the generation of representative liquid structures is critical in evaluating the NMR shielding constants of condensed-phase systems.

Benchmark Relative Energies for Large Water Clusters with the Generalized Energy-Based Fragmentation Method

The generalized energy-based fragmentation (GEBF) method has been applied to investigate relative energies of large water clusters (H2O)n (n = 32, 64) with the coupled-cluster singles and doubles with noniterative triple excitations (CCSD(T)) and second-order Møller-Plesset perturbation theory (MP2) at the complete basis set (CBS) limit. Here large water clusters are chosen to be representative structures sampled from molecular dynamics (MD) simulations of liquid water. Our calculations show that the GEBF method is capable of providing highly accurate relative energies for these water clusters in a cost-effective way. We demonstrate that the relative energies from GEBF-MP2/CBS are in excellent agreement with those from GEBF-CCSD(T)/CBS for these water clusters. With the GEBF-CCSD(T)/CBS relative energies as the benchmark results, we have assessed the performance of several theoretical methods widely used for ab initio MD simulations of liquids and aqueous solutions. These methods include density functional theory (DFT) with a number of different functionals, MP2, and density functional tight-binding (the third generation, DFTB3 in short). We find that MP2/aug-cc-pVDZ and several DFT methods (such as LC-ωPBE-D3 and ωB97XD) with the aug-cc-pVTZ basis set can provide satisfactory descriptions for these water clusters. Some widely used functionals (such as B3LYP, PBE0) and DFTB3 are not accurate enough for describing the relative energies of large water clusters. Although the basis set dependence of DFT is less than that of ab initio electron correlation methods, we recommend the combination of a few best functionals and large basis sets (at least aug-cc-pVTZ) in theoretical studies on water clusters or aqueous solutions.

Orbital Analysis and Excited-State Calculations in an Energy-Based Fragmentation Method.

Covalently bound molecular arrays composed of porphyrins or related pigments have gained a lot of interest as components of artificial light-harvesting systems and molecular photonic devices. The large size of these arrays, however, makes their theoretical investigation employing the ab initio or density functional methodologies difficult. Energy-based fragmentation methods (EBF) represent a set of conceptually simple approaches to theoretical investigation of large systems and were therefore chosen as a tool to study these systems. Here a new approach to EBF, EBF-MO, is introduced that enables one to obtain orbitals and orbital energies and to perform population analysis and excited-state calculations of large systems composed of hundreds of atoms. This approach was implemented into a parallel program, JETT, and the benchmark calculations have shown its accuracy and applicability to the ground- and excited-state calculations of systems containing transition metals and extended π-conjugation. EBF-MO was then applied to the density functional theory (DFT) and the time-dependent density functional theory (TDDFT) calculations of ground- and excited-state properties of a porphyrin-based molecular photonic wire composed of 472 atoms and 4265 basis functions at the B3LYP/LANL08,6-31G* level. The TDDFT calculations have revealed the character of the excited states, and the unidirectionality of the excitation energy transfer across the array relevant to its signal transfer function. The computational approaches introduced here have widened the applicability of the ab initio and density functional methodologies to calculations of extended systems such as natural and artificial light-harvesting systems and molecular photonic devices.

Combined Fragmentation Method: A Simple Method for Fragmentation of Large Molecules

Here we present a new energy-based fragmentation method that is based on our previous work and combines the best elements of other energy-based fragmentation methods. Our new approach, termed "combined fragmentation method", is foremost simple to implement, robust, accurate, and produces small fragments, which are independent of conformation and size of the target molecule. Essentially small collections of bonded atoms in the target molecule are assigned to groups. Fragment molecules are formed by taking all bonded pairs of these groups. These fragments are then interacted with one another, and the interaction energy is simply added to the initial fragmentation energy. The method has been tested on numerous molecules of biological interest both in vacuum and in a continuum solvent.

Accurately Reproducing Ab Initio Electrostatic Potentials with Multipoles and Fragmentation

In this work, we show that our energy based fragmentation method (Bettens, R. P. A.; Lee, A. M. J. Phys. Chem. A 2006, 110, 8777) accurately reproduces the electrostatic potential for a selection of peptides, both charged and uncharged, and other molecules of biological interest at the solvent accessible surface and beyond when compared with the full ab initio or density functional theory electrostatic potential. We also consider the ability of various point charge models to reproduce the full electrostatic potential and compare the results to our fragmentation electrostatic potentials with the latter being significantly superior. We demonstrate that our fragmentation approach can be readily applied to very large systems and provide the fragmentation electrostatic potential for the neuraminidase tetramer (ca. 24,000 atom system) at the MP2/6-311(+)G(2d,p) level. We also show that by using at least distributed monopoles, dipoles, and quadrupoles at atomic sites in the fragment molecules an essentially identical electrostatic potential to that given by the fragmentation electrostatic potential at and beyond the solvent accessible surface can be obtained.