Lanthanide metals in the boron cages: Computational prediction of M@Bn (M = Eu,Gd; n = 38, 40)

Endohedral metalloborofullerenes (EMBFs) are novel boron analogues of the famous endohedral metallofullerenes (EMFs). Many EMBFs have been proposed by theoretical calculations thus far. However, in sharp contrast to EMFs, which trap most of the lanthanides with f electrons inside the cages, the corresponding lanthanide‐based EMBFs have never been reported. In this work, the encapsulation of Eu and Gd in the B₃₈ and B₄₀ fullerenes was studied by means of density functional theory calculations. Our results revealed that Gd@B₃₈(⁹A), Eu@B₄₀(⁸B₂), and Gd@B₄₀(⁷A″) all favor the endohedral configuration, and the electronic structures can be described as Gd³⁺@ , Eu²⁺@ , and Gd³⁺@ with jailed f electron spins. The large binding energies and sizable HOMO–LUMO gaps suggest that they may be achieved experimentally. They feature σ and π double aromaticity, and their excellent stabilities were confirmed by the Born–Oppenheimer molecular dynamics simulations. Finally, the infrared and UV/vis spectra were simulated to assist experimental characterization.     

The versatility of pentalene coordination to transition metals: a density functional theory investigation

DFT calculations with full geometry optimization have been carried out on a series of real and hypothetical compounds of the type [CpM(C8H6)], [(CO)3M(C8H6)], [M(C8H6)2], [(CpM)2(C8H6)], [[(CO)3M]2(C8H6)], and [M2(C8H6)2] (M = transition metal). The bonding in all the currently known compounds is rationalized, as well as in the (so far) hypothetical stable complexes. Depending on the electron count and the nature of the metal(s), eta2 (predicted), eta3, eta5, eta8, or intermediate coordination modes can be adopted. In the case of the mononuclear species, the most favored closed-shell electron counts are 18 and 16 metal valence electrons (MVE). In the case of the dinuclear species, an electron count of 34 MVEs is most favored. However, other electron counts can be stabilized, especially in the case of dinuclear complexes. Coordinated pentalene should most often be considered as formally being a dianion, but sometimes as a neutral ligand. In the former case it can behave as an aromatic species made of two equivalent fused rings, as a C5 aromatic ring connected to an allylic anion, or even as two allylic anions bridged by a C7=C8 double bond. In the latter case, it can behave as a bond-alternating cyclic polyene or as a C5 aromatic ring connected to an allylic cation.     

椅型碳纳米管吸附氧原子的密度泛函理论研究

利用密度泛函B3LYP对有限长扶手椅形单壁碳纳米管(3,3),(4,4)和(5,5)吸附O原子的几何结构、电子属性、反应能和红外光谱进行了系统地理论研究,获得了一些有意义的结果,主要包括如下4个方面:(1)2个O原子吸附在管外壁垂直于管轴的C—C键形成开环的轮烯结构,吸附在管内壁形成环氧结构;(2)O原子吸附在管外壁要比吸附在管内壁具有较大的能隙和吸附反应能;(3)与单壁碳纳米管管外壁吸附1个O原子相比,2个O原子吸附在管外壁具有较大的吸附反应能;(4)B3LYP得到的C—O伸缩振动频率与实验一致.     

Modeling a halogen dance reaction mechanism: A density functional theory study

Since the discovery of the halogen dance (HD) reaction more than 60 years ago, numerous insights into the mechanism have been unveiled. To date however, the reaction has not been investigated from a theoretical perspective. Density functional theory (DFT) was used to model the potential energy surface linking the starting reagents to the lithiated products for each step in the mechanism using a thiophene substrate. It was found that the lithium‐halogen exchange mechanism is critical to understand the HD mechanism in detail and yielded the knowledge that S_N2 transition states (TS) are favored over the four‐center type for the lithium‐bromine exchange steps. The overall driving force for the HD is thermodynamics, while the kinetic factors tightly control the reaction path through temperature. The S_N2 lithium‐bromide TS are barrierless, except the second, which is the limiting step. Finally, the model for the HD is discovered to be a pseudo‐clock type, due to a highly favorable bromide catalysis step and the reformation of 2‐bromothiophene. © 2016 Wiley Periodicals, Inc.     

Gas-phase acidity of D-glucose. A density functional theory study

The gas-phase acidity of D-glucopyranose was studied by means of B3LYP calculations combined with 6-31G(d,p) or 6-31+G(d,p) standard basis sets. For each anomer, deprotonation of the various primary and secondary hydroxyl groups was considered. As in solution, the anomeric hydroxyl is found to be the most acidic for both anomers, but only when the 6-31+G(d,p) basis set is used for geometry optimization. Deprotonation of the anomeric hydroxyl induces an important C(1)--O endocyclic bond elongation and subsequently promotes an energetically favored ring-opening process as attested by the very small calculated activation barriers. The results also suggest that interconversion between the various deprotonated alpha- and beta-anomers may easily occur under slightly energetic conditions. B3LYP/6-311+G(2df,2p) calculations led to the an absolute gas-phase acidity of deltaacidGo(298)(alpha-D-glucose) = 1398 kJ mol(-1). This estimate matches well the only experimental value available to date. Finally, this study again confirms that the use of diffuse functions on heavy atoms is necessary to describe anionic systems properly and to achieve good relative and absolute gas-phase acidities.     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.     

A Systemic Insight into Exohedral Actinides and Endohedral Borospherenes: An&Bm and An@Bn (An=U,Np, Pu; m = 28, 32, 34, 36, 38, 40; n = 36, 38, 40)

A series of exohedral actinide borospherenes, An&B_m, and endohedral borospherenes, An@B_n (An=U, Np, Pu; m = 28, 32, 34, 36, 38, 40; n = 36, 38, 40), have been characterized by density functional theory calculations. The electronic structures, chemical bond topological properties and spectra have been systematically investigated. It was found that An@B_n is more stable than An&B_n in terms of structure and energy, and UB₃₆ in an aqueous solution is the most stable molecular in this research. The IR and UV-vis spectra of An&B_m and An@B_n are computationally predicted to facilitate further experimental investigations. Charge-transfer spectroscopy decomposes the total UV-Vis absorption curve into the contributions of different excitation features, allowing insight into what form of electronic excitation the UV–Vis absorption peak is from the perspective of charge transfer between the An atoms and borospherenes.     

Hybrid density functional theory investigation of a series of alloxan-based thiosemicarbazones and semicarbazones

Recently, the synthesis and the NMR characterization of a series of eight alloxan-based thiosemicarbazones and semicarbazones were reported. These compounds exhibit a strongly hydrogenbonded hydrazinic proton that is a part of a characteristic six-membered ring. This proton is highly deshielded and resonates far downfield in the proton NMR spectra. In this report, mPW1PW91/6-31+G(d,p) calculations have been used to investigate the structure and other molecular properties of this series of eight compounds. The relationship between the ¹H and ¹³C NMR chemical shifts and various geometric parameters was investigated, and linear relationships for proton peaks that are involved in hydrogen-bond interactions were found.     

The use of the hybrid density functional theory (DFT) approach for calculation of vibrational spectra: nitromethane

The molecular geometry of nitromethane was optimized and its force field and vibrational spectrum were calculated by the BECKE3LYP method. The accuracy of optimization of the geometry of MeNO₂ obtained by this method using the 6–311G(d,p) and 6–311++G(d,p) basis sets is not poorer than that obtained at the second-order Møller-Plesset level of perturbation theory (MP2). The vibrational frequencies of nitromethane and its d₁, d₂, and d₃ isotopomers obtained by the BECKE3LYP method are in much better agreement with the experimental data than those calculated at the MP2 level using the same basis set. The average absolute error of calculations performed without the use of any scaling factors is ～2% for frequencies; the maximum deviation is ～4%.     

Hydroformylation and isomerization of allene and propyne: a density functional theory study

The [HCo(CO)3]-catalyzed hydroformylation of allene and propyne has been investigated at the B3LYP level of density functional theory. It is found that hydroformylation of allene favors the linear anti-Markovnikov product in high regioselectivity both kinetically and thermodynamically. The origin of this regioselectivity comes from the enhanced stability of the eta3-allylic intermediate [(eta3-CH2CHCH2)Co(CO)3]. By contrast, propyne does not show any regioselectivity. The possible interconversion between allene and propyne mediated by [HCo(CO)3] has been explored.     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

A density functional theory investigation on the formation mechanisms of DNA interstrand crosslinks induced by chloroethylnitrosoureas

Chloroethylnitrosoureas (CENUs) are an important family of alkylating agents used in the clinical treatment of cancer. Their anticancer mechanism primarily involves the formation of DNA interstrand crosslinks (ICLs) induced by the chloroethyldiazonium ion derived from the decomposition of CENUs. In this work, the mechanism for the formation of ICLs was investigated by density functional theory (DFT) with B3LYP, wB97XD, and M062X functinoals using conductor‐like polarizable continuum model solvent model. Three pathways leading to the formation of three types of G–C crosslinks were compared. G(N1)–C(N3) crosslink is predicted to be the dominant crosslinking product other than G(O⁶)–C(N⁴) and G(N²)–C(O²) crosslinks, which is consistent with the previous results obtained from QM/MM computations. The results indicate that the formation of the G(N1)–C(N3) crosslink via pathway A is the most favorable mechanism from both kinetic and thermodynamic standpoints. In this pathway, the chloroethyldiazonium ion alkylates guanine on the O⁶ site followed by intramolecular cyclization to form O⁶,N1‐ethanoguanine ( 4 ). The cytosine then reacts with intermediate 4 on the C^α atom to yield the G(N1)–C(N3) crosslink. This work provides reasonable explanations for the supposed mechanism of CENUs‐induced ICLs formation obtained from experimental investigations. © 2012 Wiley Periodicals, Inc.     

左旋葡聚糖热解机理的密度泛函理论研究

采用密度泛函理论B3LYP/6-31++G(d,p)方法,对纤维素热解的主要产物左旋葡聚糖的热解反应机理进行了理论计算分析,设计了四种可能的热解反应途径, 对各种反应的反应物、产物和过渡态的结构进行了能量梯度全优化。计算结果表明,左旋葡聚糖开环成链状中间体时,首先,左旋葡聚糖中的两个半缩醛键C(1)-O(7)和C(6)-O(8)断裂,经过渡态TS₁形成中间体IM₁,同时,C(6)-O(7)结合成键使C(5)-C(6)-O(7)形成环状结构,该反应的能垒较高,为296.53 kJ/mol,然后IM₁经过渡态TS₂转变为中间体IM₂,该反应的能垒为234.09 kJ/mol;对IM₂设计了四条可能的反应路径,反应路径2和3能垒较低,是IM₂最可能的热解反应途径;在反应路径1和4中都包含了脱羰基反应,其反应能垒较高,不易发生。     

Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.     

Density functional theory of polymer-polymer phase separation behavior

Polyatomic density functional theory is applied to a binary polymer blend. The polymer reference interaction site model (PRISM) liquid state theory provides the homogeneous state correlation functions necessary for the application of density functional theory. An effective chi parameter can be recognized from the density functional expression; however, the phase separation criteria does not depend solely upon the chi parameter, rather it depends upon various combinations of the species-dependent direct correlation functions of the blend. The Flory-Huggins chi parameter along with the associated phase diagram is obtained when the monomer volumes of the blend species are equal and for a range of monomer-monomer attractive interactions. Calculations are performed both with and without the assumption of incompressibility. The density functional theory along with the PRISM determined “input” predict that an isotopic polymer blend shows an upper critical solution temperature (UCST) phenomena. © 1995 John Wiley & Sons, Inc.     

PyCDFT: A Python package for constrained density functional theory

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn–Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097 .     

黄酮类化合物的密度泛函理论研究

在混合密度泛函B3LYP理论下,用6-31G*基函数研究了几种典型黄酮类化合物分子的几何结构、电子结构和分子的静电势,讨论了电子结构和分子活性部位的关系.     

氢化可的松和表氢化可的松的密度泛函理论研究

采用密度泛函理论B3LYP/6-31G和B3LYP/6-311G*方法优化了氢化可的松和表氢化可的松的几何结构,利用优化的结构得到了氢化可的松和表氢化可的松的原子净电荷、总能量及前沿分子轨道组成.基于简谐振动分析求得了氢化可的松和表氢化可的松的红外光谱频率和强度,由统计热力学分析得到了热力学函数;进而确定了氢化可的松和...     

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn–Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518–2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097–3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn–Sham matrix formation. © 2019 Wiley Periodicals, Inc.     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007