An ab initio quantum chemical comparative study of possible additive rules and linear relations in parent and extended sulfur diimide families

In this study, it has been demonstrated that there are additive rules corresponding to ab initio derived total electronic energies between members of triple sets of some extended sulfur diimides and their mono- and bi-derivatives. It has been shown that the additive rules are insensitive to the combination of methods and basis sets used to derive the total electronic energies. This insensitivity to the level of calculation is demonstrated to be the case for some linear alkanes also. It has been found that the total electronic energies of certain members of extended sulfur diimide sets ((ZZ)_k and (EE)_k conformers) follow a linear relation although chemical accuracy may be achieved only by excluding the smallest members of these sets. The details of this deviation have been employed to quantify the “Z-effect” proposed previously by the same authors.     

Assessing conformer energies using electronic structure and machine learning methods

We have performed a large‐scale evaluation of current computational methods, including conventional small‐molecule force fields; semiempirical, density functional, ab initio electronic structure methods; and current machine learning (ML) techniques to evaluate relative single‐point energies. Using up to 10 local minima geometries across ~700 molecules, each optimized by B3LYP‐D3BJ with single‐point DLPNO‐CCSD(T) triple‐zeta energies, we consider over 6500 single points to compare the correlation between different methods for both relative energies and ordered rankings of minima. We find that the current ML methods have potential and recommend methods at each tier of the accuracy‐time tradeoff, particularly the recent GFN2 semiempirical method, the B97‐3c density functional approximation, and RI‐MP2 for accurate conformer energies. The ANI family of ML methods shows promise, particularly the ANI‐1ccx variant trained in part on coupled‐cluster energies. Multiple methods suggest continued improvements should be expected in both performance and accuracy.     

Electronic Structure Research on Lattice Stability of V,Nb, and Ta by Density Functional Theory

The difference of energy and electronic structure of V, Nb, and Ta in different crystalline structures were investigated by different methods in density functional theory (DFT). Latticeconstants, total energies, and densities of states of these metals were calculated using the plane-wave pseudopotential method in DFT. Results were compared with those of projector augmented wave method, CALPHAD method, and experiments. Total energy and electronic structure analyses showed that valence electrons mostly transferred from s to p or d state, changing obviously with both the crystal structure and the elemental period number from V to Ta and leading to stronger cohesion, higher cohesive energy and more stable lattice of heavier metals.     

Testing the pairwise additive potential approximation using DFT: coadsorption of CO and N on Rh (100).

The interaction between adsorbates is a key issue in surface science, because these interactions can influence strongly the properties of chemisorbed species with consequences for the thermodynamics and kinetics of surface processes. The simplest representation of adsorbate-adsorbate interactions is based on the assumption that all interactions are pairwise additive. This approach has been satisfactorily used in the modeling of temperature-programmed desorption (TPD) spectra using both continuum and Monte Carlo methods. However, the energies estimated within the pairwise approximation have never been compared to the energies calculated using density functional theory (DFT) methods. We demonstrate that the pairwise additive potential approximation is indeed a good representation of the adsorbate-adsorbate interactions, and that we do not need to include three-body interactions or higher-order terms to estimate the perturbation of the adsorption energy of an adsorbate by the presence of other coadsorbates. Moreover, we show for the first time how DFT can be used to explain the desorption features that one finds in TPD experiments, thus linking the TPD desorption features with actual microscopic configurations.     

有机半导体的电子电离能、亲和势和极化能的密度泛函理论研究

准确预测有机半导体的能级(如电子电离能和亲和势等)对设计新型有机半导体材料和理解相关机理至关重要。从理论计算的角度看,主要挑战来自于缺少一种不仅能够在定性上合理而且在定量上精确预测,同时并不显著增加计算成本的理论方法。本文中,我们证明了通过结合极化连续介质模型(PCM)和"最优调控"区间分离密度泛函方法能够准确预测一系列有机半导体的电子电离能(IP)、亲和势(EA)和极化能,其预测结果与实验数据吻合得很好。重要的是,经过调控后分子的前线分子轨道能量(即-~εHOMO和-~εLUMO)与对应的IP和EA计算值很接近。调控方法的成功可以进一步归因于其能够根据不同分子体系或同种分子所处的不同状态(气态和固态)"最优"地平衡泛函中分别用于描述电子局域化和离域化的作用。相比而言,其它常见的密度泛函方法由于包含的HF%比例过低(如PBE)或过高(如M06HF和未调控的区间分离泛函),均不能给予合理的预测。因此,我们相信这种PCM-调控的方法能够为研究其它更加复杂的有机体系的能级问题提供一种更加可靠和便捷的理论工具。     

Self‐consistent field for fragmented quantum mechanical model of large molecular systems

Fragment‐based linear scaling quantum chemistry methods are a promising tool for the accurate simulation of chemical and biomolecular systems. Because of the coupled inter‐fragment electrostatic interactions, a dual‐layer iterative scheme is often employed to compute the fragment electronic structure and the total energy. In the dual‐layer scheme, the self‐consistent field (SCF) of the electronic structure of a fragment must be solved first, then followed by the updating of the inter‐fragment electrostatic interactions. The two steps are sequentially carried out and repeated; as such a significant total number of fragment SCF iterations is required to converge the total energy and becomes the computational bottleneck in many fragment quantum chemistry methods. To reduce the number of fragment SCF iterations and speed up the convergence of the total energy, we develop here a new SCF scheme in which the inter‐fragment interactions can be updated concurrently without converging the fragment electronic structure. By constructing the global, block‐wise Fock matrix and density matrix, we prove that the commutation between the two global matrices guarantees the commutation of the corresponding matrices in each fragment. Therefore, many highly efficient numerical techniques such as the direct inversion of the iterative subspace method can be employed to converge simultaneously the electronic structure of all fragments, reducing significantly the computational cost. Numerical examples for water clusters of different sizes suggest that the method shall be very useful in improving the scalability of fragment quantum chemistry methods. © 2015 Wiley Periodicals, Inc.     

Approximate ab initio energies by systematic molecular fragmentation

A scheme is introduced for generating a hierarchy of molecular fragmentations by which the total electronic energy can be approximated from the energies of the fragments. Higher levels in the hierarchy produce molecular fragments of larger size and approximate the total electronic energy more reliably. A correction to account for nonbonded interactions is also presented. The accuracy of the approach is tested for a number of examples, and shown to be essentially independent of the level of ab initio theory employed. The computational cost increases linearly with the size of the molecule.     

Electron delocalization in linearly pi-conjugated systems: a concept for quantitative analysis

Donor- and/or acceptor-substituted pi-conjugated systems represent an important class of compounds in organic chemistry. However, up to now, a general method to quantitatively address the efficiency of a conjugated path is still missing. In this work, a novel computational approach based on deletion energies and on second-order orbital interaction energies in a natural bond orbital (NBO) scheme is employed to quantitatively assess ("measure") delocalization energies. Moreover, the purpose of this work is to assess the efficiency of distinct pi-conjugated paths, that is, geminal, cis, and trans, as well as to predict the impact of substituents on a given backbone. This study is focused on various mono-, di-, tri-, and tetrasubstituted tetraethynylethenes (TEEs). These model systems are suitable for our analysis, because they offer distinct conjugation paths within the same molecule, and can also be substituted in multiple ways. Differences between conjugation paths, the effect of neighbor paths, and the impact of donor and acceptor substituents on the various paths are discussed.     

Transition levels of defects in ZnO: Total energy and Janak's theorem methods

Transition levels of defects are commonly calculated using either methods based on total energies of defects in relevant charge states or energy band single particle eigenvalues. The former method requires calculation of total energies of charged, perfect bulk supercells, as well as charged defect supercells, to obtain defect formation energies for various charge states. The latter method depends on Janak's theorem to obtain differences in defect formation energies for various charge states. Transition levels of V(Zn), V(O), and V(ZnO) vacancy defects in ZnO are calculated using both methods. The mean absolute deviation in transition level calculated using either method is 0.3 eV. Relative computational costs and accuracies of the methods are discussed.     

New accurate reference energies for the G2/97 test set

A recently proposed computational protocol is employed to obtain highly accurate atomization energies for the full G2/97 test set, which consists of 148 diverse molecules. This computational protocol is based on the explicitly correlated coupled-cluster method with iterative single and double excitations as well as perturbative triple excitations, using quadruple-ζ basis sets. Corrections for higher excitations and core/core-valence correlation effects are accounted for in separate calculations. In this manner, suitable reference values are obtained with a mean deviation of -0.75 kJ/mol and a standard deviation of 1.06 kJ/mol with respect to the active thermochemical tables. Often, in the literature, new approximate methods (e.g., in the area of density functional theory) are compared to, or fitted to, experimental heats of formation of the G2/97 test set. We propose to use our atomization energies for this purpose because they are more accurate on average.     

Comparison of some representative density functional theory and wave function theory methods for the studies of amino acids

Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-311++G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-311++G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-311++G(d,p), aug-cc-pVDZ, 6-311++G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-311++G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.     

Performance of SCAN density functional for a set of ionic liquid ion pairs

Computational chemistry is a powerful tool for the discovery of novel materials. In particular, it is used to simulate ionic liquids in search of electrolytes for electrochemical applications. Herein, the choice of the computational method is not trivial, as it has to be both efficient and accurate. Density functional theory methods with appropriate corrections for the systematic weaknesses can give precision close to that of the post‐Hartree–Fock coupled cluster methods with a fraction of their cost. Thence, we have evaluated the performance of a recently developed nonempirical strongly constrained and appropriately normed (SCAN) density functional on electronic structure calculations of ionic liquid ion pairs. The performance of SCAN and other popular functionals (PBE, M06‐L, B2PLYP) among with Grimme's dispersion correction and Boys–Bernardi basis set superposition error correction was compared to DLPNO‐CCSD(T)/CBS. We show that SCAN reproduces coupled‐cluster results for describing the employed dataset of 48 ion pairs.     

Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning

Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.

Low scaling quantum mechanics calculations and machine learning can be employed to efficiently predict the molecular energies, forces, and optical and electrical properties of molecular materials and their aggregates.     

Accuracy and efficiency of electronic energies from systematic molecular fragmentation

A systematic method for approximating the ab initio electronic energy of molecules from the energies of molecular fragments is tested on a large sample of typical organic molecular structures. The detailed methods, including some additional refinements for molecular rings and long range interactions, are described. The accuracy and computational efficiency of the systematic hierarchy of methods are reported.     

On the calculation of correlation energies in the spin-density functional formalism

It is shown that dynamical correlation effects can be adequately treated using the local spin-density approximation. The computational effort is very small compared to CI calculations. The method is applied to correlation energies and ionization potentials of the atoms Li to Ar and binding energies of the diatomic hydrides LiH to HCl.     

Correlated geminal wave function for molecules: an efficient resonating valence bond approach

We show that a simple correlated wave function, obtained by applying a Jastrow correlation term to an antisymmetrized geminal power, based upon singlet pairs between electrons, is particularly suited for describing the electronic structure of molecules, yielding a large amount of the correlation energy. The remarkable feature of this approach is that, in principle, several resonating valence bonds can be dealt simultaneously with a single determinant, at a computational cost growing with the number of electrons similar to more conventional methods, such as Hartree-Fock or density functional theory. Moreover we describe an extension of the stochastic reconfiguration method, which was recently introduced for the energy minimization of simple atomic wave functions. Within this extension the atomic positions can be considered as further variational parameters, which can be optimized together with the remaining ones. The method is applied to several molecules from Li(2) to benzene by obtaining total energies, bond lengths and binding energies comparable with much more demanding multiconfiguration schemes.     

硝酸甲酯分子间相互作用的DFT和ab initio比较

用密度泛函理论(DFT)和从头算(ab initio)方法,分别在B3LYP/6 31G和HF/6 31G水平上求得硝酸甲酯三种二聚体的全优化几何构型和电子结构,并用6 311G和6 311＋＋G基组进行总能量计算.对HF/6 31G计算结果进行MP4SDTQ电子相关校正.在各基组下均进行基组叠加误差(BSSE)和零点能(ZPE)校正求得结合能.对6 31G优化构型作振动分析并基于统计热力学求得200～600 K温度下单体和二聚体的热力学性质.详细比较两种方法的相应计算结果,发现DFT求得的分子间距离较短,分子内键长较长,所得结合能均小于相应ab initio计算值.     

Complete basis set ab initio computational study of ionization potential, electron affinity and the C-F bond dissociation energy for perfluorinated methane derivatives

A computational study of perfluorinated methane derivatives was performed with complete basis set ab initio methods. The total energies for their neutral, cation, and anionic states were computed. From these values, the energy gaps between different electronic states, ionization potentials, electron affinities, and C-F bond dissociation energies were calculated. The computed values are compared with experimental data and the reliability of complete basis set ab initio methods is discussed. New values for C-F bond dissociation energies are suggested. Received: 12 January 1998 / Accepted: 2 April 1998 / Published online: 29 July 1998     

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Two related methods to calculate the Kohn-Sham correlation energy within the framework of the adiabatic-connection fluctuation-dissipation theorem are presented. The required coupling-strength-dependent density-density response functions are calculated within exact-exchange time-dependent density-functional theory, i.e., within time-dependent density-functional response theory using the full frequency-dependent exchange kernel in addition to the Coulomb kernel. The resulting resolution-of-identity exact-exchange random-phase approximation (RI-EXXRPA) methods in contrast to previous EXXRPA methods employ an auxiliary basis set (RI basis set) to improve the computational efficiency, in particular, to reduce the formal scaling of the computational effort with respect to the system size N from N(6) to N(5). Moreover, the presented RI-EXXRPA methods, in contrast to previous ones, do not treat products of occupied times unoccupied orbitals as if they were linearly independent. Finally, terms neglected in previous EXXRPA methods can be included, which leads to a method designated RI-EXXRPA+, while the method without these extra terms is simply referred to as RI-EXXRPA. Both EXXRPA methods are shown to yield total energies, reaction energies of small molecules, and binding energies of noncovalently bonded dimers of a quality that is similar and in some cases even better than that obtained with quantum chemistry methods such as Mo?ller-Plesset perturbation theory of second order (MP2) or with the coupled cluster singles doubles method. In contrast to MP2 and to conventional density-functional methods, the presented RI-EXXRPA methods are able to treat static correlation.     

用密度泛函和遗传算法研究Cun (n≤20) 团簇的尺寸效应

结合遗传算法和Gupta多体势系统地搜索金属团簇Cu_n (n≤20)的几何结构, 并利用密度泛函方法进一步确定最稳定构型. 分析了平均键长、平均配位数、结合能、二阶差分能、电离势和电子亲和势等性质随着尺寸的变化规律. 发现在Cu₇处团簇最稳定构型从二维结构转向三维结构, Cu_n (n≤20)团簇的幻数为8, 13, 20. 团簇的键长、配位数和结合能属性随着尺寸的增长而递增最终接近相应的体相值; 而二阶差分能、电离势和电子亲和势随着尺寸增加出现奇偶交替, 说明偶数电子形成闭壳层结构, 比相邻团簇更稳定.