Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

大体系分区密度泛函计算方法

提出一种新的对大体系进行分区密度泛函计算的方法。将大体系划分为若干较小的区,每个小区是一个相对独立的量子力学子体系,计及其它区势场的影响和电子的Pauli排斥作用,可以进行相对独立的密度泛函计算。对各子体系求解单电子方程：(F^k F^kp)C^k=S^kC^kε^k K=A,B,C,…式中F^k,C^k,S^k,ε^k分别为子体系K的Fbck矩阵、轨道系数矩阵、基组重叠矩阵和本征值矩阵,F^kb起强制属于不同子体系的占据轨道之间保持正交的作用。得到的轨道是分区定域化的,汇总各区的计算结果得出整个体系的电子结构信息。通过对一些较大分子的计算,考察了几种因素对分区计算精度的影响。结果表明,提出的方法是可行的,通过控制各区基组的大小,可以基本消除基组截断误差,得到精确的计算结果。对于足够大的体系,本方法是一种线性标度算法;和文献报道的相关方法比较,更容易用于对体系的某些区域进行特别的计算研究。     

Molecular structure and binding energies of monosubstituted hexacarbonyls of chromium,molybdenum, and tungsten: Relativistic density functional study

Relativistic density functional calculations have been carried out for the group VI transition metal carbonyls M(CO)₅L (M=Cr, Mo, W; L=OH₂, NH₃, PH₃, PMe₃, N₂, CO, OC (isocarbonyl), CS, CH₂, CF₂, CCl₂, NO⁺). The optimized molecular structures and M(SINGLE BOND)L bond dissociation energies, as well as the metal–carbonyl bond energy of the trans CO group, have been calculated. Besides the marked dependence of the trans M(SINGLE BOND)CO bond length on the type of ligand L, such an effect on the that bond energy is also observed. For the chromium compounds, the trans Cr(SINGLE BOND)CO bond length varies from 184 to 199 pm and its bond energy from 242 to 150 kJ/mol. For the molybdenum compounds, the range is 197 to 216 pm and 253 to 128 kJ/mol and, for tungsten, 198 to 214 pm and 293 to 159 kJ/mol. The observed trends can be explained with the π acceptor strength of the L ligand. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1985–1992, 1997     

Density functional finite cluster method for polarizability of large BeN three‐dimensional systems

The structures and the properties of small clusters are known to be quite different from those of the bulk material. Consequently, the focus of most studies is towards understanding the changes in electronic properties with increasing cluster size. Linear static electronic dipole polarizabilities of the Be_N (N→∞) solid are obtained at the DFT(PWB91) level by extrapolation of ab initio calculations on Be_N (N=1,…,132) clusters. For the mean polarizability, a [5s3p] basis set is shown to give accurate values if the tri‐periodic clusters are big enough. No calculation has yet been carried out on Be_N (N→∞), but it is clear that these linear properties converge relatively slowly with cluster size. For Be_N, cluster size up to N=90 atoms are sufficient to give limiting infinite solid polarizabilities with relatively small uncertainties. For N=132, the mean polarizability result is probably very accurate. These results suggest that DFT is a good method for the determination of these properties. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 230–240, 2001     

Molecular structure and vibrational spectra of phenobaraitone by density functional theory and ab initio hartree-Fock calculations

Quantum chemistry calculations have been performed using Gaussian03 program to compute optimized geometry, harmonic vibrational frequency along with intensities in IR and Raman spectra at RHF/6-31++G** and B3LYP/6-31++G** levels for phenobarbitone (C₁₂H₁₂N₂O₃) in the ground state. The scaled harmonic vibrational frequencies have been compared with experimental FT-IR and FT-Raman spectra. Theoretical vibrational spectra of the title compound were interpreted by means of potential energy distributions (PEDs) using MOLVIB program. A detailed interpretation of the infrared spectra of the title compound is reported. On the basis of the agreement between the calculated and observed results, the assignments of fundamental vibrational modes of phenobarbitone were examined and some assignments were proposed. The theoretical spectrograms for FT-IR and FT-Raman spectra of the title compound have been constructed.     

Density functional calculations on the conversion of azide and carbon monoxide to isocyanate and dinitrogen by a nickel to sulfur rebound mechanism

Density functional calculations (B3 LYP & BP86) on a model system for the reaction between carbon monoxide and [Ni(N(3))('S(3)')](-) ('S(3)'(2-)=bis(2-mercaptophenyl)sulfide (2-)) predict a three-step mechanism. First, CO attacks the nickel to generate a pseudo "square-pyramidal" complex, in which CO, N(3) (-), and two sulfides are basal and the central S atom of the 'S(3)'(2-) ligand backs away from Ni to form a weak Ni-S apical bond. Then, CO inserts into the Ni-N bond and the weak apical Ni--S bond rebounds to its original strength as the nickel forms a square-planar intermediate. Finally, in a one-step process N(2) leaves as the remaining N atom and carbonyl rearrange to produce the nickel isocyanate product [Ni(NCO)('S(3)')](-).     

An assessment of pure,hybrid, meta,and hybrid‐meta GGA density functional theory methods for open‐shell systems: The case of the nonheme iron enzyme 8R–LOX

The performance of a range density functional theory functionals combined in a quantum mechanical (QM)/molecular mechanical (MM) approach was investigated in their ability to reliably provide geometries, electronic distributions, and relative energies of a multicentered open‐shell mechanistic intermediate in the mechanism 8R–Lipoxygenase. With the use of large QM/MM active site chemical models, the smallest average differences in geometries between the catalytically relevant quartet and sextet complexes were obtained with the B3LYP^* functional. Moreover, in the case of the relative energies between ⁴II and ⁶II , the use of the B3LYP^* functional provided a difference of 0.0 kcal mol^–1. However, B3LYP^± and B3LYP also predicted differences in energies of less than 1 kcal mol^–1. In the case of describing the electronic distribution (i.e., spin density), the B3LYP^*, B3LYP, or M06‐L functionals appeared to be the most suitable. Overall, the results obtained suggest that for systems with multiple centers having unpaired electrons, the B3LYP^* appears most well rounded to provide reliable geometries, electronic structures, and relative energies. © 2012 Wiley Periodicals, Inc.     

A Density Matrix Renormalization Group Study of the Low-Lying Excited States of a Molybdenum Carbonyl-Nitrosyl Complex

A density matrix renormalization group-self consistent field (DMRG-SCF) study has been carried out to calculate the low-lying excited states of CpMo(CO)₂NO, a molybdenum complex containing NO and CO ligands. In order to automatically select an appropriate active space, a novel procedure employing the maximum single-orbital entropy for several states has been introduced and shown to be efficient and easy-to-implement when several electronic states are simultaneously considered. The analysis of the resulting natural transition orbitals and charge-transfer numbers shows that the lowest five excited electronic states are excitation into metal-NO antibonding orbitals, which offer the possibility for nitric oxide (NO) photorelease after excitation with visible light. Higher excited states are metal-centered excitations with contributions of metal-CO antibonding orbitals, which may serve as a gateway for carbon monoxide (CO) delivery. Time-dependent density functional theory calculations done for comparison, show that the state characters agree remarkably well with those from DMRG-SCF, while excitation energies are 0.4–1.0 eV red-shifted with respect to the DMRG-SCF ones.     

Density functional study of neutral and anionic AlO(n) and ScO(n) with high oxygen content

The electronic and geometrical structures of neutral and negatively charged AlO₅, AlO₆, AlO₇, AlO₈, AlO₉, AlO₁₀, AlO₁₁, AlO₁₂, AlO₁₅, AlO₁₆, and AlO₁₈ along with the corresponding series of ScO_n and ScO oxides were investigated using density functional theory with generalized gradient approximation. We found that these species possess geometrically stable isomers for all values of n = 5–12, 15, 16, 18 and are thermodynamically stable for n = 5–7. The species with n = 16 are found to be octa‐dioxides M(η¹‐O₂)₈ while the species with n = 15 and 18 are penta‐ozonides (η²‐O₃)M(η¹‐O₃)₄ and hexa‐ozonides M(η¹‐O₃)₆, respectively. Geometrical configurations of a number of the lowest total energy states of Al and Sc oxides are different. Especially, drastic differences are found for the anion AlO and ScO pairs at n = 9, 10, and 11. The Sc? O bonds are longer than the Al? O bonds by ≈0.2 Å, which, in turn, slightly affects the corresponding interoxygen bond lengths. The charges on metal atoms are close to +2e in both Al series and to +1.5e in both Sc series. As an extra electron is delocalized over ligands in the presence of a large positive charge on the metal atom of the anions, the electron affinity (EA) of the neutrals along with the ionization energies of the anions are large and exceed the EAs of the halogen atoms in a number of cases. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

乙炔基自由基C2H与氧气反应的密度泛函理论研究

应用量子化学从头算和密度泛函理论(DFT)对C₂H自由基和O₂的反应进行了研究.在B3LYP/6-311G^**水平上优化了反应通道上各驻点(反应物、中间体、过渡态和产物)的几何构型,并计算出它们的振动频率和零点振动能(ZPVE).各物种的总能量由CCSD(T)/6-311G^**//B3LYP/6-311G^**给出,并对能量进行了零点能校正.计算结果表明,反应物中自由基C₂H中的边端C进攻O₂形成了中间体1 (HCCOO),中间体1是一个加合产物.由中间体1经过不同的反应通道可以生成不同的产物P₁ (HCO+CO), P₂ (HCCO+O), P₃(CO₂+CH), P₄ (C₂O+OH)和P₅ (2CO+H).反应通道之间存在着竞争机制.其中P₁, P₂是主要产物,其次还有一定比例的P5生成,而产物P₃, P₄的生成几率较低.各条反应通道化学反应热的计算与实验吻合较好.     

Density Functional Theory Study on the Adsorption of CN on Transition Metal M（100） （M = Ni,Pd, Pt,Cu, Ag and Au） Surfaces

The adsorption of cyanide on the top site of a series of transition metal M（100） （M = Cu, Ag, Au, Ni, Pd, Pt） surfaces via carbon and nitrogen atoms respectively, with the CN axis perpendicular to the surface, has been studied by means of density functional theory and cluster model. Geometry, adsorption energy and vibrational frequencies have been determined, and the present calculations show that the adsorption of CN through C-end on metal surface is more favorable than that via N-end for the same surface. The vibrational frequencies of CN for C-down configuration on surface are blue-shifted with respect to the free CN, which is contrary to the change of vibrational frequencies when CN is adsorbed by N-down structure. Furthermore, the charge transfer from surface to CN causes the increase of surface work function.     

Crystal structures and electronic properties of BaC_2 isomers by theoretical study based on DFT

Band structures and electronic properties of two BaC2 isomers were calculated by using density func-tional theory(DFT) properly.The ionic bond features are all typical between cation(Ba) and anion clusters(C2) in both structures of the isomers.However,a much stronger covalent bond exists in anion clusters which can be seen by inspecting the electron distribution contour that has a dull bell like shape between two carbon atoms.The shortest distance between Ba2 and C22? and the bond length in anion clusters are different in these isomers of BaC2,which are 0.2945 nm and 0.1185 nm for the structure with the I4/mmm space group and 0.2744 and 0.1136 nm with the C2/c type,respectively.Band structures were clarified by combining the DOS to indicate the ionic bonding features more clearly.Population analysis provided further evidence on these ideas.Thermodynamical calculation results reveal that the transition temperature of these two polymorphs of BaC2 locates near 132 K,which is consistent with the recent experimental results.     

Density functional theory studies on the dissociation energies of metallic salts: relationship between lattice and dissociation energies

The formation and physicochemical properties of polymer electrolytes strongly depend on the lattice energy of metal salts. An indirect but efficient way to estimate the lattice energy through the relationship between the heterolytic bond dissociation and lattice energies is proposed in this work. The heterolytic bond dissociation energies for alkali metal compounds were calculated theoretically using the Density Functional Theory (DFT) of B3LYP level with 6‐311+G(d,p) and 6‐311+G(2df,p) basis sets. For transition metal compounds, the same method was employed except for using the effective core potential (ECP) of LANL2DZ and SDD on transition metals for 6‐311+G(d,p) and 6‐311+G(2df,p) calculations, respectively. The dissociation energies calculated by 6‐311+G(2df,p) basis set combined with SDD basis set were better correlated with the experimental values with average error of ca. ±1.0% than those by 6‐311+G* combined with the LANL2DZ basis set. The relationship between dissociation and lattice energies was found to be fairly linear (r>0.98). Thus, this method can be used to estimate the lattice energy of an unknown ionic compound with reasonably high accuracy. We also found that the dissociation energies of transition metal salts were relatively larger than those of alkaline metal salts for comparable ionic radii. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 827–834, 2001     

BF3活化高锰酸氧化丙烯酸反应机理的 密度泛函研究

用量子化学密度泛函理论(DFT)的B3LYP方法对高锰酸根离子与丙烯酸的环加成反应机理进行了系统研究, 全参数优化了反应势能面上各驻点的几何构型、振动频率和能量. 计算结果表明: 反应有两个竞争通道, 即[2+3]反应通道和[2+2]反应通道, 其中[2+3]通道比[2+2]通道的反应势垒降低了183.89 kJ/mol, 并通过在高锰酸根的氧原子上配位一个或两个BF3分子来研究BF3分子对反应体系的活化效应, 结合两个BF3分子使得[2+3]通道的反应势垒降低为23.97 kJ/mol, 则有利于反应按该通道进行, 然而[2+2]通道的反应势垒仍较高(>195 kJ/mol).这进一步表明该反应体系中加入一定量BF3能提高高锰酸氧化烯烃双键的化学活性.     

Crystal structures and electronic properties of BaC<Subscript>2</Subscript> isomers by theoretical study based on DFT

Band structures and electronic properties of two BaC₂ isomers were calculated by using density functional theory (DFT) properly. The ionic bond features are all typical between cation (Ba) and anion clusters (C₂) in both structures of the isomers. However, a much stronger covalent bond exists in anion clusters which can be seen by inspecting the electron distribution contour that has a dull bell like shape between two carbon atoms. The shortest distance between Ba²⁺ and C₂²⁻ and the bond length in anion clusters are different in these isomers of BaC₂, which are 0.2945 nm and 0.1185 nm for the structure with the I4/mmm space group and 0.2744 and 0.1136 nm with the C2/c type, respectively. Band structures were clarified by combining the DOS to indicate the ionic bonding features more clearly. Population analysis provided further evidence on these ideas. Thermodynamical calculation results reveal that the transition temperature of these two polymorphs of BaC₂ locates near 132 K, which is consistent with the recent experimental results. Supported by the National Natural Science Foundation of China (Grant No. 50361003) and the Natural Science Foundation of Yunnan Province (Grant No. 2006003Z) and Science Innovation Foundation of Kunming University of Science and Technology     

吡咯和呋喃气相质子化过程的密度泛函理论研究

Density functional theory and ab initio calculations have been used to determine structures and stabilities of the protonated aromatics species AH^＋ and AH2^2＋ （A=pyrrole, furan）. Possible mechanisms and relative energetics for protonation of pyrrole and furan by H3O^＋ and AH^＋ in the gas phase have been explored. Calculations show that the Cα-protonated species was the most stable structure for AH^＋, and the protonated AH^＋ might accommodate the second proton to yield AH2^2＋ if the free proton was available. The gas-phase H3O^＋ could protonate pyrrole and furan with significant exothermiCity and almost without barrier. The proton transfer from AH4^＋ to pyrrole and furan has a barrier ranging from 33.5 to 39.3 kJ/mol in the gas phase.     

BF_3活化高锰酸氧化丙烯酸反应机理的密度泛函研究

用量子化学密度泛函理论(DFT)的B3LYP方法对高锰酸根离子与丙烯酸的环加成反应机理进行了系统研究,全参数优化了反应势能面上各驻点的几何构型、振动频率和能量.计算结果表明:反应有两个竞争通道,即[2+3]反应通道和[2+2]反应通道,其中[2+3]通道比[2+2]通道的反应势垒降低了183.89kJ/mol,并通过在高锰酸根的氧原子上配位一个或两个BF3分子来研究BF3分子对反应体系的活化效应,结合两个BF3分子使得[2+3]通道的反应势垒降低为23.97kJ/mol,则有利于反应按该通道进行,然而[2+2]通道的反应势垒仍较高(195kJ/mol).这进一步表明该反应体系中加入一定量BF3能提高高锰酸氧化烯烃双键的化学活性.     

Density functional embedded cluster study of Cu(4), Ag(4) and Au(4) species interacting with oxygen vacancies on the MgO(001) surface

Cu(4), Ag(4), and Au(4) species adsorbed on an MgO(001) surface that exhibits neutral (F(s)) and charged (F(s) (+)) oxygen vacancies have been studied using a density functional approach and advanced embedding models. The gas-phase rhombic-planar structure of the coinage metal tetramers is only moderately affected by adsorption. In the most stable surface configuration, the plane of the tetramers is oriented perpendicular to the MgO(001) surface; one metal atom is attached to an oxygen vacancy and another one is bound to a nearby surface oxygen anion. A very similar structural motif was recently found on defect-free MgO(001), where two O(2-) ions serve as adsorption sites. Following the trend of the interactions with the regular MgO(001) surface, Au(4) and Cu(4) bind substantially stronger to F(s) and F(s) (+) sites than Ag(4). This stronger adsorption interaction at oxygen vacancies, in particular at F(s), is partly due to a notable accumulation of electron density on the adsorbates. We also examined the propensity of small supported metal species to aggregate to adsorbed di-, tri- and tetramers. Furthermore, we demonstrated that core-level ionization potentials offer the possibility for detecting experimentally supported metal tetramers and characterizing them structurally with the help of calculated data.     

Theoretical Study on the Dehydrogenation Reaction of H2S by VS+ (3∑-)

The dehydrogenation reaction of H2S by the 3∑- ground state of VS+: VS+ + H2S → VS2+ + H2 has been studied by using Density Functional Theory (DFT) at the B3LYP/DZVP level. It is found that the reaction proceeds along two possible pathways (A and B) yielding two isomer dehydrogenation products VS2+-1 (3B2) and VS2+-2 (3A1), respectively. For both pathways,the reaction has a two-step-reaction mechanism that involves the migration of two hydrogen atoms from S2 to V+, respectively. The migration of the second hydrogen via TS3 and that of the first via TS4 are the rate-determining steps for pathways A and B, respectively. The activation energy is 17.4 kcal/mol for pathway A and 22.8 kcal/mol for pathway B relative to the reactants. The calculated reaction heat of 9.9 kcal/mol indicates the endothermicity of pathway A and that of -11.9 kcal/mol suggests the exothermicity of pathway B.