Generalized Energy-based Fragmentation Approach Research Articles

Generalized Energy-Based Fragmentation Approach for the Electronic Emission Spectra of Large Systems.

The excited-state (ES) geometry optimization and electronic emission (fluorescence and phosphorescence) spectra and the ES vibrational spectra of large systems are great challenges in quantum chemistry. In this work, we develop a generalized energy-based fragmentation (GEBF) approach to compute the localized ES structures and vibrational frequencies of large systems. In this approach, the ES energy derivatives (gradients or Hessians) for a localized ES of a large system can be obtained by combining the ES energy derivatives of the corresponding active subsystems (including local excitation center) and the ground-state energy derivatives of inactive subsystems. Two strategies are adopted to overcome two difficulties from state-classification and state-tracking for treating specific ESs. First, for state-classification, we develop an improved density-based spatial clustering applied with noise algorithm with a modified transition orbital projection (TOP) algorithm, which allow a certain ES energy and energy derivatives of the whole system to be calculated with different ES energies and energy derivatives of active subsystems. Furthermore, we also employ the TOP algorithm for tracking the ESs in their geometry optimizations at the time-dependent density functional theory (TDDFT) level. Then, the GEBF approach is applied to investigate the optimized ES geometries or ES vibrational frequencies for two typical systems. Our results show that the cost-effective GEBF approach can accurately reproduce the TDDFT fluorescence spectra of the cytosine derivative and the experimental phosphorescence spectra of the β-cyclodextrin derivative. The GEBF approach is expected to be routinely applied to investigate the electronic emission spectra of very large systems with local chromophores.

Structures and Spectroscopic Properties of Large Molecules and Condensed-Phase Systems Predicted by Generalized Energy-Based Fragmentation Approach.

ConspectusThe structures and spectroscopic properties of molecules and condensed-phase systems are usually experimentally characterized by X-ray, infrared (IR), Raman, nuclear magnetic resonance (NMR), and electronic absorption/emission spectra. Quantum mechanics (QM) calculations are critical in quantitatively understanding the relationship between the structure and physicochemical properties of various chemical systems. However, it is very challenging to apply traditional QM methods to large molecules and condensed-phase systems with large unit cells due to their steep computational scaling with the system size. To overcome this difficulty, theoretical chemists have developed various linear (or low) scaling QM methods, among which energy-based fragmentation methods have achieved great success for large molecules or clusters. One of the most popular energy-based fragmentation methods is the generalized energy-based fragmentation (GEBF) approach developed by us.In this approach, the ground-state energy of a large molecule can be evaluated from the ground-state energies of a series of embedded subsystems. In this Account, we focus on the recent developments and applicability of the GEBF approach for the structures and spectroscopic properties of complicated large molecules and condensed-phase systems. With new fragmentation schemes, the GEBF approach can now describe ionic liquid clusters and metal-containing supramolecular systems accurately and can provide accurate binding energies for host-guest complexes. In addition, the GEBF approach is now available for describing the localized excited states of large systems including a chromophore. More importantly, the GEBF approach under periodic boundary conditions (PBC-GEBF) has been developed to deal with periodic molecular crystals and liquids. Then, the ground-state energy (or property) per unit cell of a periodic condensed phase system can be predicted with QM calculations on nonperiodic embedded subsystems. This feature enables accurate electron correlation calculations on molecular crystals and liquids to be feasible on ordinary workstations. The PBC-GEBF approach has been applied to predict the crystal structures, lattice energies, and spectroscopic properties of some typical molecular crystals and solutions. By combining the GEBF method and machine learning (ML) method, a GEBF-ML force field has been developed for long normal alkanes, and the IR spectra of long alkanes can be obtained from the GEBF-ML molecular dynamics (MD) simulations. The GEBF and its periodic variant are expected to play increasingly important roles in investigating real-life chemical systems of broad interests at the ab initio levels.

Improved generalized energy-based fragmentation approach and its applications to the binding energies of supramolecular complexes

Accurate prediction for the binding energies of host–guest complexes is important in the field of supramolecular chemistry. In this article, we have implemented an improved generalized energy-based fragmentation (GEBF) approach for computing the binding energies of supramolecular complexes. In this approach, a new scheme is proposed to generate primitive GEBF subsystems with reasonable size. With this scheme, those subsystems in the complex and the corresponding host molecule are very similar (the guest does not exist in any subsystem of host). Our results for ten supramolecular complexes show that the improved GEBF approach could accurately reproduce the conventional density functional theory (DFT) binding energies in those complexes. The GEBF binding energy errors relative to the corresponding conventional values are usually less than 1 kcal mol−1. Furthermore, for each pair of complexes with the same or similar hosts, the GEBF relative binding energy difference between the two complexes with different guests is even below 1 kJ mol−1. In addition, the GEBF approach could predict the second-order Møller–Plesset perturbation theory (MP2) energy of a complex with 3382 basis functions within only 3.3 h by massive parallelization using 312 processors on 13 computer nodes. Therefore, the improved GEBF approach could be a practical tool for predicting the binding energies or relative binding energies of supramolecular complexes.

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.

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.

Generalized Energy-Based Fragmentation Approach for Localized Excited States of Large Systems.

We have extended the generalized energy-based fragmentation (GEBF) approach to localized excited states of large systems. In this approach, the excited-state energy of a large system could be expressed as the combination of the excited-state energies of "active subsystems", which contains the chromophore center, and the ground-state energies of "inactive subsystems". The GEBF approach has been implemented at the levels of time-dependent density functional theory (TDDFT) and approximate coupled cluster singles and doubles (CC2) method. Our results show that GEBF-TDDFT can reproduce the TDDFT excitation energies and solvatochromic shifts for large systems and that GEBF-CC2 could be used to validate GEBF-TDDFT result (with different functionals). The GEBF-TDDFT method is found to be able to provide satisfactory or reasonable descriptions on the experimental solvatochromic shifts for the n → π* transitions of acetone in various solutions, and the lowest π → π* transitions of pyridine and uracil in aqueous solutions.

Ab initio molecular dynamics with intramolecular noncovalent interactions for unsolvated polypeptides

Ab inito molecular dynamics (AIMD) based on the generalized energy-based fragmentation (GEBF) approach is employed for the ultrafast conformational dynamics of two unsolvated polypeptides, $$3_{10}$$ -helical acetyl(ala) $$_{18}\hbox {NH}_2$$ and a subunit of DNA polymerase $$\beta$$ . In the GEBF approach, the energies and energy gradients of subsystems are obtained with M06-2X functionals, which can describe intramolecular noncovalent interaction. The results are compared with those obtained from the simulations based on AMBER99 and CHARMM22 force fields, and semiempirical density-functional tight-binding (DFTB) and DFTB with empirical dispersion correction (DFTB-D) methods. Our results show that the GEBF-M06-2X simulations may provide reasonable results for the conformational changes of the two unsolvated polypeptides due to the description of intramolecular noncovalent interactions. The AMBER99, CHARMM22, DFTB, and DFTB-D simulations give quite different results. The GEBF-M06-2X-based AIMD simulations are expected to be applied to the fast or ultrafast conformational dynamics of large unsolvated polypeptides and to be employed for improving the empirical force fields.

LSQC: Low scaling quantum chemistry program

A low scaling quantum chemistry program, called LSQC, is described in this article. This version includes two linear scaling methods, generalized energy‐based fragmentation (GEBF) approach and cluster‐in‐molecule (CIM) approach. In the GEBF approach, a variety of electron structure methods (including ab initio and density functional theory) are available for the calculations of ground‐state energies, geometry optimizations, vibrational spectra, and other molecular properties for large systems. In the CIM approach, the electron correlation energies of large systems can be approximately obtained at the second‐order Møller−Plesset perturbation theory and couple cluster levels. In this article, the details and the capabilities of the LSQC program are presented. © 2014 Wiley Periodicals, Inc.

Generalized energy-based fragmentation approach and its applications to macromolecules and molecular aggregates.

Conspectus The generalized energy-based fragmentation (GEBF) approach provides a very simple way of approximately evaluating the ground-state energy or properties of a large system in terms of ground-state energies of various small "electrostatically embedded" subsystems, which can be calculated with any traditional ab initio quantum chemistry (X) method (X = Hartree-Fock, density functional theory, and so on). Due to its excellent parallel efficiency, the GEBF approach at the X theory level (GEBF-X) allows full quantum mechanical (QM) calculations to be accessible for systems with hundreds and even thousands of atoms on ordinary workstations. The implementation of the GEBF approach at various theoretical levels can be easily done with existing quantum chemistry programs. This Account reviews the methodology, implementation, and applications of the GEBF-X approach. This method has been successfully applied to optimize the structures of various large systems including molecular clusters, polypeptides, proteins, and foldamers. Such investigations could allow us to elucidate the origin and nature of the cooperative interaction in secondary structures of long peptides or the driving force of the self-assembly processes of aromatic oligoamides. These GEBF-based QM calculations reveal that the structures and stability of various complex systems result from a subtle balance of many types of noncovalent interactions such as hydrogen bonding and van der Waals interactions. The GEBF-based ab initio molecular dynamics (AIMD) method also allows the investigation of dynamic behaviors of large systems on the order of tens of picoseconds. It was demonstrated that the conformational dynamics of two model peptides predicted by GEBF-based AIMD are noticeably different from those predicted by the classical force field MD method. With the target of extending QM calculations to molecular aggregates in the condensed phase, we have implemented the GEBF-based multilayer hybrid models, which could provide satisfactory descriptions of the binding energies between a solute molecule and its surrounding waters and the chain-length dependence of the conformational changes of oligomers in aqueous solutions. A coarse-grained polarizable molecular mechanics model, furnished with GEBF-X dipole moments of subsystems, exhibits some advantages of treating the electrostatic polarization with reduced computational costs. We anticipate that the GEBF approach will continue to develop with the ultimate goal of studying complicated phenomena at mesoscopic scales and serve as a practical tool to elucidate the structure and dynamics of chemical and biological systems.

The Generalized Energy‐Based Fragmentation Approach with an Improved Fragmentation Scheme: Benchmark Results and Illustrative Applications

We propose an improved fragmentation scheme for the generalized energy-based fragmentation (GEBF) approach, which improves the accuracy of the GEBF approach in total energy calculations and intermolecular interactions. The main modification is to introduce some two-fragment-centered primitive subsystems, which are neglected in the previous GEBF implementation. Numerical calculations demonstrate that the present GEBF approach can provide more accurate ground-state energies and intermolecular interactions. The present GEBF approach with the M06-2X functional and the cc-pVTZ basis set are employed to investigate the structures and binding energies in two dimeric species, which are related to pseudopolymorphism of a phenyleneethynylene-based π-conjugated molecule. A comparison of the binding free energies in a dimeric species and its corresponding model without C-H···F contacts reveal that the substitution of fluorine atoms weakens the binding of monomers in the dimeric species formed by intermolecular O-H···O hydrogen bonds, but strengthens the binding in the dimer formed by the π-π stacking interaction. Therefore, the C-H···F contacts in these two dimeric species are demonstrated to play a less significant role.

An Efficient Implementation of the Generalized Energy-Based Fragmentation Approach for General Large Molecules

An efficient implementation of the generalized energy-based fragmentation (GEBF) approach (Li, W.; Li, S.; Jiang, Y. J Phys. Chem. A 2007, 111, 2193) for treating a wide range of large molecules is presented. In this implementation, the fragmentation process can be automatically done for a general molecule, with only some functional groups defined by users. A new and fast scheme is designed for the generation of various subsystems and the derivation of their coefficients. The newly implemented GEBF approach has been applied to several large molecules including proteins, nucleic acids, and supermolecules with fused aromatic rings. Test calculations within the Hartree-Fock (HF) and density functional theory (DFT) framework demonstrate that the GEBF approach can provide reasonably accurate ground-state energies and optimized structures, which are in good agreement with those from conventional HF or DFT calculations. The GEBF approach implemented in this work can now be employed by nonexpert users to compute energies, optimized structures, and some molecular properties at various ab initio levels for a broad range of large molecules on ordinary PC workstations.

Geometry Optimizations and Vibrational Spectra of Large Molecules from a Generalized Energy-Based Fragmentation Approach

The generalized energy-based fragmentation (GEBF) approach (Li, W.; Li, S.; Jiang, Y. J. Phys. Chem. A 2007, 111, 2193) is extended for geometry optimizations and vibrational spectra calculations of general large molecules or clusters. In this approach, the total energy and its derivatives, and some molecular properties, of a target system are obtained from conventional calculations on a series of subsystems derived from the target system. Each subsystem is electronically embedded in the background point charges generated by all other atoms outside the subsystem so that the long-range interactions and polarization effects between remote fragments are approximately taken into account. The approach computationally scales linearly with the system size and can be easily implemented for large-scale parallelization. By comparing the results from the conventional and GEBF calculations for several test molecules including a polypeptide and a water cluster, we demonstrate that the GEBF approach is able to provide quite reliable predictions for molecular geometries, vibrational frequencies, and thermochemistry data and satisfactory descriptions for vibrational intensities, for general molecules with polar or charged groups.