普适的基于能量的分块局域激发态聚类算法

在普适的基于能量的分块(GEBF)方法的框架下, 大体系的局域激发(LE)能可通过一系列活性子体系激发能的线性组合近似得到, 从而有效降低了计算的时间标度. 然而, 在体系的局域激发具有多个激发态的情形下, 如何有效识别所有活性子体系的激发特征并将其组合是一个挑战. 提出了一种基于局域激发态聚类的算法. 该方案基于空穴-电子分析和基于密度的聚类(DBSCAN)机器学习算法, 可以自动地聚合不同子体系中最相似的激发态并组合得到相应的局域激发态能量或激发能. 结合该算法改进的LE-GEBF方法在荧光分子衍生物、 荧光染料-水团簇及绿色荧光蛋白模型体系的计算中均获得了令人满意的结果. 该算法有望大大提升LE-GEBF方法在计算局域激发时的稳定性和准确性, 并可以有效处理吸收光谱具有多重峰的大体系.     

A localized molecular-orbital assembler approach for Hartree-Fock calculations of large molecules

We describe an alternative fragment-based method, the localized molecular-orbital assembler method, for Hartree-Fock (HF) calculations of macromolecules. In this approach, a large molecule is divided into many small-size fragments, each of which is capped by its local surroundings. Then the conventional HF calculations are preformed on these capped fragments (or subsystems) and the canonical molecular orbitals of these systems are transferred into localized molecular orbitals (LMOs). By assembling the LMOs of these subsystems into a set of LMOs of the target molecule, the total density matrix of the target molecule is constructed and correspondingly the HF energy or other molecular properties can be approximately computed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations with double-zeta and polarized double-zeta basis sets demonstrate that the present approach is able to reproduce the conventional HF energies within a few millihartrees for a broad range of molecules.     

An efficient fragment-based approach for predicting the ground-state energies and structures of large molecules

An efficient fragment-based approach for predicting the ground-state energies and structures of large molecules at the Hartree-Fock (HF) and post-HF levels is described. The physical foundation of this approach is attributed to the "quantum locality" of the electron correlation energy and the HF total energy, which is revealed by a new energy decomposition analysis of the HF total energy proposed in this work. This approach is based on the molecular fractionation with conjugated caps (MFCC) scheme (Zhang, D. W.; Zhang, J. Z. H. J. Chem. Phys. 2003, 119, 3599), by which a macromolecule is partitioned into various capped fragments and conjugated caps formed by two adjacent caps. We find that the MFCC scheme, if corrected by the interaction between non-neighboring fragments, can be used to predict the total energy of large molecules only from energy calculations on a series of small subsystems. The approach, named as energy-corrected MFCC (EC-MFCC), computationally achieves linear scaling with the molecular size. Our test calculations on a broad range of medium- and large molecules demonstrate that this approach is able to reproduce the conventional HF and second-order Moller-Plesset perturbation theory (MP2) energies within a few millihartree in most cases. With the EC-MFCC optimization algorithm described in this work, we have obtained the optimized structures of long oligomers of trans-polyacetylene and BN nanotubes with up to about 400 atoms, which are beyond the reach of traditional computational methods. In addition, the EC-MFCC approach is also applied to estimate the heats of formation for a series of organic compounds. This approach provides an appealing approach alternative to the traditional additivity rules based on either bond or group contributions for the estimation of thermochemical properties.     

DCMB that combines divide‐and‐conquer and mixed‐basis set methods for accurate geometry optimizations,total energies,and vibrational frequencies of large molecules

We present a method, named DCMB, for the calculations of large molecules. It is a combination of a parallel divide‐and‐conquer (DC) method and a mixed‐basis (MB) set scheme. In this approach, atomic forces, total energy and vibrational frequencies are obtained from a series of MB calculations, which are derived from the target system utilizing the DC concept. Unlike the fragmentation based methods, all DCMB calculations are performed over the whole target system and no artificial caps are introduced so that it is particularly useful for charged and/or delocalized systems. By comparing the DCMB results with those from the conventional method, we demonstrate that DCMB is capable of providing accurate prediction of molecular geometries, total energies, and vibrational frequencies of molecules of general interest. We also demonstrate that the high efficiency of the parallel DCMB code holds the promise for a routine geometry optimization of large complex systems. © 2012 Wiley Periodicals, Inc.     

Fragment occupations in partition Density Functional Theory

The exact ground-state energy and density of a molecule can in principle be obtained via Partition Density Functional Theory (PDFT), a method for calculating molecular properties from Kohn-Sham calculations on isolated fragments. For a given choice of fragmentation, unique fragment densities are found by requiring that the sum of fragment energies be minimized subject to the constraint that the fragment densities sum to the correct molecular ground-state density. We investigate two interrelated aspects of PDFT: the connections between fragment densities obtained via different choices of fragmentation, for which we find "near-additivity", and the nature of their corresponding fragment occupations. Whereas near-integer occupations arise for very large inter-fragment separations, strictly integer occupations appear for small inter-fragment separations. Cases where the fragment chemical potentials cannot be equalized lead to fragment occupations that lock into integers.     

An Extended Group Function Model for Intermolecular Interactions

An extended group function model is introduced for the calculation of intermolecular interactions. The model is formulated within the framework of the energy incremental scheme. In the calculation of intra- and intersystem energies, model systems are introduced. To each subsystem is associated a set of partner subsystems defined by a vicinity criterion. In the independent calculation of intra- and intersystem energies, calculations are performed on model systems defined by the subsystems considered and their partner subsystems. To further reduce computation time, dual basis sets are introduced. A small and a large basis set are associated with each subsystem. For partner subsystems in a model system, the small basis set is adopted. Test calculations are performed on helium atoms in one- and two-dimensional lattices.     

A fragment energy assembler method for Hartree-Fock calculations of large molecules

We present a fragment energy assembler approach for approximate Hartree-Fock (HF) calculations of macromolecules. In this method, a macromolecule is divided into small fragments with appropriate size, and then each fragment is capped by its neighboring fragments to form a subsystem. The total energy of the target system is evaluated as the sum of the fragment energies of all fragments, which are available from conventional HF calculations on all subsystems. By applying the method to a broad range of molecules, we demonstrate that the present approach could yield satisfactory HF energies for all studied systems.     

O(NlogN) continuous electrostatics method for fast calculation of solvation energies of biomolecules

We report the development of a new, fast, surface-based method for numerical calculations of the solvation energy of biomolecules with a large number of charged groups. The procedure scales linearly with the system size, both in time and memory requirements, produces explicit values for the reaction field potential and stable values of the polar energy within only a few percent error margin practically for any molecular configurations. The method works well both for large and small molecules and thus gives stable energy differences for quantities such as the polar energy contributions to molecular complex formation energies.     

Divide-and-conquer local correlation approach to the correlation energy of large molecules

A divide-and-conquer local correlation approach for correlation energy calculations on large molecules is proposed for any post-Hartree-Fock correlation method. The main idea of this approach is to decompose a large system into various fragments capped by their local environments. The total correlation energy of the whole system can be approximately obtained as the summation of correlation energies from all capped fragments, from which correlation energies from all adjacent caps are removed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations for a wide range of molecules using the 6-31G or 6-31G( * *) basis set demonstrate that this simple approach recovers more than 99.0% of the conventional second-order Moller-Plesset perturbation theory and coupled cluster with single and double excitations correlation energies.     

Self-consistent embedded clusters: Building block equations for localized orthogonal orbitals

In order to be able to study a large electronic system following a building block approach, in which smaller tractable subsystems are handled at a time rather than the system as a whole, equations are proposed in this paper whose solutions are variational orthogonal orbitals localized on the subsystems. The equations for a given subsystem correspond to a molecular cluster embedded in the field created by the rest of the system, and are coupled to the corresponding equations for all subsystems under consideration, so that they must be solved self-consistently. While the localized nature of the solutions makes the equations appropriate for use in conjunction with local basis sets in practical implementations without significant loss of precision due to truncation errors, their orthogonality properties allow for the use of the advantages of the theory of separability of McWeeny in order to calculate total energies and (generalized product) wave functions. Since the building block equations proposed involve inter-subsystem interactions very cumbersome to calculate, an approximation is proposed in order to make their application to actual problems feasible: the representation of the cumbersome interaction operators by ab initio model potentials which are obtained directly from them, without resorting to any parametrization procedure based on a reference. This ab initio model potential approximation has been found to provide considerable computational savings without significant loss of accuracy in frozen-core calculations on molecules and frozen-lattice calculations on imperfect crystals.     

An ab initio study of the fcc and hcp structures of helium

The hexagonal close packed (hcp) and face centered cubic (fcc) structures of helium are studied by using a new ab initio computational model for large complexes comprising small subsystems. The new model is formulated within the framework of the energy incremental scheme. In the calculation of intra- and intersystem energies, model systems are introduced. To each subsystem associated is a set of partner subsystems defined by a vicinity criterion. In the independent calculations of intra- and intersystem energies, the calculations are performed on model subsystems defined by the subsystems considered and their partner subsystems. A small and a large basis set are associated with each subsystem. For partner subsystems in a model system, the small basis set is adopted. By introducing a particular decomposition scheme, the intermolecular potential is written as a sum of effective one-body potentials. The binding energy per atom in an infinite crystal of atoms is the negative value of this one-body potential. The one-body potentials for hcp and fcc structures are calculated for the following nearest neighbor distances (d0): 4.6, 5.1, 5.4, 5.435, 5.5, 5.61, and 6.1 a.u. The equilibrium distance is 5.44 a.u. for both structures. The equilibrium dimer distance is 5.61 a.u. For the larger distances, i.e., d0 > 5.4 a.u., the difference of the effective one-body potentials for the two structures is less than 0.2 microE(h). However, the hcp structure has the lowest effective one-body potential for all the distances considered. For the smallest distance the difference in the effective one-body potential is 3.9 microE(h). Hence, for solid helium, i.e., helium under high pressure, the hcp structure is the preferred one. The error in the calculated effective one-body potential for the distance d0 = 5.61 a.u. is of the order of 1 microE(h) (approximately 0.5%).     

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.     

Box size effects are negligible for solvation free energies of neutral solutes

Hydration free energy calculations in explicit solvent have become an integral part of binding free energy calculations and a valuable test of force fields. Most of these simulations follow the conventional norm of keeping edge length of the periodic solvent box larger than twice the Lennard-Jones (LJ) cutoff distance, with the rationale that this should be sufficient to keep the interactions between copies of the solute to a minimum. However, for charged solutes, hydration free energies can exhibit substantial box size-dependence even at typical box sizes. Here, we examine whether similar size-dependence affects hydration of neutral molecules. Thus, we focused on two strongly polar molecules with large dipole moments, where any size-dependence should be most pronounced, and determined how their hydration free energies vary as a function of simulation box size. In addition to testing a variety of simulation box sizes, we also tested two LJ cut-off distances, 0.65 and 1.0 nm. We show from these simulations that the calculated hydration free energy is independent of the box-size as well as the LJ cut-off distance, suggesting that typical hydration free energy calculations of neutral compounds indeed need not be particularly concerned with finite-size effects as long as standard good practices are followed.     

Electrostatic field-adapted molecular fractionation with conjugated caps for energy calculations of charged biomolecules

An electrostatic field-adapted molecular fractionation with conjugated caps (EFA-MFCC) approach is implemented for treating macromolecules with several charge centers. The molecular fragmentation is performed in an "electrostatic field," which is described by putting point charges on charge centers, directly affecting the Hamiltonians of both fragments and conjugated caps. So the present method does not need truncation during the calculation of electrostatic interactions. Our test calculations on a series of charged model systems and biological macromolecules using the HF and B3LYP methods have demonstrated that this approach is capable of describing the electronic structure with accuracy comparable to other fragment-based methods. The EFA-MFCC approach is an alternative way for predicting the total energies of charged macromolecules with acyclic, loop, and intersectional loop structures and interaction energies between two molecules.     

Contributions of pauli repulsions to the energetics and physical properties computed in QM/MM methods

Conventional combined quantum mechanical/molecular mechanical (QM/MM) methods lack explicit treatment of Pauli repulsions between the quantum‐mechanical and molecular‐mechanical subsystems. Instead, classical Lennard‐Jones (LJ) potentials between QM and MM nuclei are used to model electronic Pauli repulsion and long‐range London dispersion, despite the fact that the latter two are inherently of quantum nature. Use of the simple LJ potential in QM/MM methods can reproduce minimal geometries and energies of many molecular clusters reasonably well, as compared to full QM calculations. However, we show here that the LJ potential cannot correctly describe subtle details of the electron density of the QM subsystem because of the neglect of Pauli repulsions between the QM and MM subsystems. The inaccurate electron density subsequently affects the calculation of electronic and magnetic properties of the QM subsystem. To explicitly consider Pauli interactions with QM/MM methods, we propose a method to use empirical effective potentials on the MM atoms. The test case of the binding energy and magnetic properties of a water dimer shows promising results for the general application of effective potentials to mimic Pauli repulsions in QM/MM calculations. © 2013 Wiley Periodicals, Inc.     

Charged-cell periodic DFT simulations via an impurity model based on density embedding: Application to the ionization potential of liquid water

Calculations of charged systems in periodic boundary conditions (PBC) are problematic because there are spurious interactions between the charges in different periodic images that can affect the physical picture. In addition, the intuitive limit of Coulomb interactions decaying to zero as the interacting charges are placed at infinite separation no longer applies, and for example total energies become undefined. Leveraging subsystem density functional theory (also known as density embedding) we define an impurity model that embeds a finite neutral or charged subsystem within an extended (infinite) surrounding subsystem. The combination of the impurity model and a consistent choice of the Coulomb reference provides us with an algorithm for evaluating the ionization potential (IP) in extended systems. We demonstrate our approach in a pilot calculation of the IP of liquid water, based on a configuration from a prior ab initio molecular dynamics (AIMD) simulation of liquid water (Genova et al., J. Chem. Phys. 2016, 144, 234105). The calculations with the impurity model capture the broadening on the ionization energies introduced by the interactions between the water molecules. Furthermore, the calculated average IP value (10.5 eV) compare favorably to experiments (9.9-10.06 eV) and very recent simulations based on the GW approximation (10.55 eV), while at the same time outperforming density embedding calculations carried out with a naïve handling of the electrostatic interactions (about 7 eV).     

Assessing group-based cutoffs and the Ewald method for electrostatic interactions in clusters and in saturated,superheated, and supersaturated vapor phases of dipolar molecules

Monte Carlo simulations in the canonical, isobaric-isothermal, grand canonical, and Gibbs ensembles were used to assess whether the computationally expensive Ewald summation method for the computation of the first-order electrostatic energy can be replaced with a simpler truncation approach for accurate simulations of the saturated, superheated, and supersaturated vapor phases of dipolar and hydrogen-bonding molecules. Rotationally averaged hydrogen fluoride dimer and trimer energies, thermophysical properties and aggregation in the superheated vapor phase of hydrogen fluoride, nucleation free energy barriers for water, and the vapor–liquid coexistence properties of hydrogen fluoride and water were investigated over a wide range of state points. We find that for densities not too close to the critical density, results obtained from simulations using a spherical potential truncation based on neutral groups (molecules or fragments) for the Coulomb interactions are statistically identical to those obtained using the Ewald summation method. Use of the simpler spherical truncation results in a significant reduction of the computational effort for simulations employing molecular mechanics force fields and also allows for straightforward implementation of many-body expansion methods to compute the potential energy from electronic structure calculations of subsystems of the entire vapor-phase system.     

ZINDO calculations of the ground state and electronic transitions in the tetracyanonickelate Ion,Ni(CN)(4)(2-)

ZINDO semiempirical calculations on the Ni(CN)(4)(2-) ion were performed, and ground-state energies for all 41 valence-orbital-based MOs and orbital transition components of the two lowest energy fully allowed electronic transitions are reported. Gaussian 94 was used to calculate ground-state energies as a comparison. The ground-state energies using ZINDO compare much more favorably with those found through ab initio techniques than with those from a reported INDO calculation. The found electronic transitions agree substantially with earlier assignments with the exception that several orbital transitions are required to adequately model the lowest energy allowed x,y-polarized experimental transition. Calculation parameters were optimized to give excellent agreement with experiment and may serve well for more complex arrangements of this ion.     

Evolution of the electronic structure of Be clusters

Using a modified symbiotic genetic algorithm approach and many-body interatomic potential derived from first principles, we have calculated equilibrium geometries and binding energies of the ground-state and low-lying isomers of Be clusters containing up to 41 atoms. Molecular-dynamics study was also carried out to study the frequency of occurrence of the various geometrical isomers as these clusters are annealed during the simulation process. For a selected group of these clusters, higher-energy isomers were more often found than their ground-state structures due to large catchment areas. The accuracy of the above ground-state geometries and their corresponding binding energies were verified by carrying out separate ab initio calculations based on molecular-orbital approach and density-functional theory with generalized gradient approximation for exchange and correlation. The atomic orbitals were represented by a Gaussian 6-311G** basis, and the geometry optimization was carried out using the GAUSSIAN 98 code without any symmetry constraint. While the ground-state geometries and their corresponding binding energies obtained from ab initio calculations do not differ much from those obtained using the molecular-dynamics approach, the relative stability of the clusters and the energy gap between the highest occupied and the lowest unoccupied molecular orbitals show significant differences. The energy gaps, calculated using the density-functional theory, show distinct shell closure effects, namely, sharp drops in their values for Be clusters containing 2, 8, 20, 34, and 40 electrons. While these features may suggest that small Be clusters behave free-electron-like and, hence, are metallic, the evolution of the structure, binding energies, coordination numbers, and nearest-neighbor distances do not show any sign of convergence towards the bulk value. We also conclude that molecular-dynamics simulation based on many-body interatomic potentials may not always give the correct picture of the evolution of the structure and energetics of clusters although they may serve as a useful tool for obtaining starting geometries by efficiently searching a large part of the phase space.