Generalized Energy-based Fragmentation Research Articles

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates.

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Accurate and Efficient Prediction of Post-Hartree-Fock Polarizabilities of Condensed-Phase Systems.

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

Predicting the structures and vibrational spectra of molecular crystals containing large molecules with the generalized energy-based fragmentation approach.

The generalized energy-based fragmentation (GEBF) approach under periodic boundary conditions (PBCs) has been developed to facilitate calculations of molecular crystals containing large molecules. The PBC-GEBF approach can help predict structures and properties of molecular crystals at different theory levels by performing molecular quantum chemistry calculations on a series of non-periodic subsystems constructed from the studied systems. A more rigorous formula of the forces on translational vectors of molecular crystals was proposed and implemented, enabling more reliable predictions of crystal structures. Our benchmark results on several typical molecular crystals show that the PBC-GEBF approach could reproduce the forces on atoms and the translational vectors and the optimized crystal structures from the corresponding conventional periodic methods. The improved PBC-GEBF approach is then applied to predict the crystal structures and vibrational spectra of two molecular crystals containing large molecules. The PBC-GEBF approach can provide a satisfactory description on the crystal structure of a molecular crystal containing 312 atoms in a unit cell at density-fitting second-order Møller-Plesset perturbation theory and density functional theory (DFT) levels and the infrared vibrational spectra of another molecular crystal containing 864 atoms in a unit cell at the DFT level. The PBC-GEBF approach is expected to be a promising theoretical tool for electronic structure calculations on molecular crystals containing large molecules.

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.

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 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.

Generalized energy-based fragmentation approach for accurate binding energies and Raman spectra of methane hydrate clusters

Methane hydrates (MHs) play important roles in the fields of chemistry, energy, environmental sciences, etc. In this work, we employ the generalized energy-based fragmentation (GEBF) approach to compute the binding energies and Raman spectra of various MH clusters. For the GEBF binding energies of various MH clusters, we first evaluated the various functionals of density functional theory (DFT), and compared them with the results of explicitly correlated combined coupled-cluster singles and doubles with noniterative triples corrections [CCSD(T)(F12*)] method. Our results show that the two best functionals are B3PW91-D3 and B97D, with mean absolute errors of only 0.27 and 0.47 kcal/mol, respectively. Then we employed GEBF-B3PW91-D3 to obtain the structures and Raman spectra of MH clusters with mono- and double-cages. Our results show that the B3PW91-D3 functional can well reproduce the experimental C−H stretching Raman spectra of methane in MH crystals, with errors less than 3 cm−1. As the size of the water cages increased, the C−H stretching Raman spectra exhibited a redshift, which is also in agreement with the experimental “loose cage−tight cage” model. In addition, the Raman spectra are only slightly affected by the neighboring environment (cages) of methane. The blueshifts of C−H stretching frequencies are no larger than 3 cm−1 for CH4 from monocages to doublecages. The Raman spectra of the MH clusters could be combined with the experimental Raman spectra to investigate the structures of methane hydrates in the ocean bottom or in the interior of interstellar icy bodies. Based on the B3PW91-D3 or B97D functional and machine learning models, molecular dynamics simulations could be applied to the nucleation and growth mechanisms, and the phase transitions of methane hydrates.

Generalized energy-based fragmentation approach for calculations of solvation energies of large systems.

A generalized energy-based fragmentation (GEBF) approach has been combined with a universal solvation model based on solute electron density (SMD) to compute the solvation energies of general large systems (such as protein molecules) in solutions. In the GEBF-SMD method, the solvation energy of a target system could be combined by the corresponding solvation energies of various subsystems, each of which is embedded in the background point charges and surface charges on the surface of solute cavity at the positions of its atoms and neighbouring atoms outside of the subsystem. Our results show that the GEBF-SMD model could reproduce the conventional SMD solvation energies quite well for various proteins in solutions, and could significantly reduce the computational costs for the SMD calculations of large proteins. In addition, the GEBF-SMD approach is almost independent of the basis sets and the types of solvents (including protic, polar, and nonpolar ones). Also, the GEBF-SMD approach could reproduce the relative energies of various conformers of large systems in solutions. Therefore, the GEBF-SMD method is expected to be applicable for computing the solvation energies of a broad range of large systems.

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.

An On-the-Fly Approach to Construct Generalized Energy-Based Fragmentation Machine Learning Force Fields of Complex Systems.

An on-the-fly fragment-based machine learning (ML) approach was developed to construct machine learning force fields for large complex systems. In this approach, the energy, forces, and molecular properties of the target system are obtained by combining machine learning force fields of various subsystems with the generalized energy-based fragmentation (GEBF) approach. Using a nonparametric Gaussian process (GP) model, all the force fields of subsystems are automatically generated online without data selection and parameter optimization. With the GEBF-ML force field constructed for a normal alkane, C60H122, long-time molecular dynamics (MD) simulations are performed on different sizes of alkanes, and the predicted energy, forces, and molecular properties (dipole moment) are favorably comparable with full quantum mechanics (QM) calculations. The predicted IR spectra also show excellent agreement with the direct ab initio MD results. Our results demonstrate that the GEBF-ML method provides an automatic and efficient way to build force fields for a broad range of complex systems such as biomolecules and supramolecular systems.

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.

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.

How intermolecular interactions influence electronic absorption spectra: insights from the molecular packing of uracil in condensed phases.

The photoexcitation mechanism in photochemistry and photophysics is a key to understanding the photostability and photoreaction of nucleobases. Using a combination of the generalized energy-based fragmentation (GEBF) and quantum mechanical and molecular mechanical (GEBF-QM/MM) approach and the QM/MM approach, we have investigated the electronic absorption spectra for the π-π* transition of uracil in aqueous solution, amorphous solid, and crystal. Our results indicate that the intermolecular interactions in terms of molecular packing are crucial for the investigation of the absorption spectra of uracil in different environments. There is a large red-shift (relative to uracil in the gas-phase) for uracil in the amorphous phase, which arises from hydrogen-bonding (HB) and close π-π stacking interactions. In contrast, the relatively smaller red-shift of uracil in aqueous solution can be attributed to the cooperative HB and long-range electrostatic and polarization interactions. Due to the HB and weak π-π interactions, the red-shift of the crystal is smaller than that of amorphous uracil. Furthermore, the results suggest that a large system is required to obtain the accurate absorption spectra of solutions, whereas small electrostatically embedded cluster models could be used to obtain the corresponding results for amorphous solids and molecular crystals.

THz spectra and corresponding vibrational modes of DNA base pair cocrystals and polynucleotides

The generalized energy-based fragmentation (GEBF) approach has been applied to study the THz spectra and vibrational modes of base pair cocrystals under periodic boundary conditions (denoted as PBC-GEBF). Results of vibrational mode reveal that hydrogen bonds play a pivotal role in the pairing process of base crystals, where most NH and CH bonds stretch to some extent. We also found that hydrogen bonds of a self-made A:T cocrystal completely break in a transition from liquid to the solid state, while self-made C:G cocrystal is different and easier to form a cocrystal, as confirmed by X-ray diffraction (XRD) and terahertz (THz) spectra. Furthermore, we have studied DNA polynucleotides (in both A and B forms) found that the vibrational modes changed a lot during the process of their forming double strand. Despite the key role played by hydrogen bonds, the key contribution originates from collective motions of the main skeleton. A comparative study of the spectra of some stranded fragments suggests that different sequences or forms have similar spectra in THz band. They distinguish from each other mainly in the low-frequency regions, especially below 1 THz. This study would make great contributions to the molecular dynamics model based DNA long-chain structure simulation in the future study.

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.

Generalized energy‐based fragmentation approach for modeling condensed phase systems

We have extended the generalized energy‐based fragmentation (GEBF) method to condensed phase systems with periodic boundary condition (PBC). The so‐called PBC‐GEBF method provides an alternative way of calculating electronic structures of condensed phase systems, whose accuracy is comparable to standard periodic electronic structure methods for some types of condensed phase systems such as molecular crystals and ionic liquid crystals. Within the PBC‐GEBF approach, the unit cell energy (or properties) of a condensed phase system can be evaluated as a linear combination of ground‐state energies (or corresponding properties) of a series of electrostatically embedded subsystems, which can be routinely calculated with existing molecular quantum chemistry packages. With the PBC‐GEBF approach, one can routinely perform ab initio calculations at post‐Hartree–Fock levels, including Møller–Plesset perturbation theory (MP2) or coupled cluster singles and doubles, on certain types of condensed phase systems, in which periodic post‐Hartree–Fock methods are not available or not feasible computationally. This review will offer an overview of the methodology and implementation of the PBC‐GEBF method and its applications in predicting the structures, lattice energies, and vibrational spectra of a wide range of molecular and ionic liquid crystals. Our results show that the PBC‐GEBF approach at post‐Hartree–Fock theory level can generally provide highly accurate descriptions on the structure and properties of crystals under study. For example, the vibrational spectra of the crystalline BH3NH3 predicted by the PBC‐GEBF approach at the MP2 level are in better agreement with the experimentally observed spectra, than those based on density functional theory calculations. WIREs Comput Mol Sci 2017, 7:e1297. doi: 10.1002/wcms.1297This article is categorized under: Structure and Mechanism &gt; Molecular Structures

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.