Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.     

Substitution Effect in NICS Values in Tropylium Ion Derivatives: An Ab Initio Study

Hartree–Fock (HF) and hybrid density functional theory (B3LYP) calculations were performed on tropylium ion and 19 of its mono- and diheteroatomic derivatives. The aromaticity in this class of compounds is evaluated based on the nucleus independent chemical shift (NICS) values. The NICS values are calculated at the center of the rings NICS (0) and at 1Å above the molecular plane NICS (1). The geometry optimization and NICS calculations were carried out at the HF/6–311+G?? and at the B3LYP/6–311+G (2d, p) density functional level, respectively. These calculations in the effects of heteroatoms such as N, B, P, and Si are considered on aromaticity, molecular properties, NICS values, and structural parameters.     

Hybrid density functional theory for pi-stacking interactions: application to benzenes, pyridines, and DNA bases

The suitability of a hybrid density functional to qualitatively reproduce geometric and energetic details of parallel pi-stacked aromatic complexes is presented. The hybrid functional includes an ad hoc mixture of half the exact (HF) exchange with half of the uniform electron gas exchange, plus Lee, Yang, and Parr's expression for correlation energy. This functional, in combination with polarized, diffuse basis sets, gives a binding energy for the parallel-displaced benzene dimer in good agreement with the best available high-level calculations reported in the literature, and qualitatively reproduces the local MP2 potential energy surface of the parallel-displaced benzene dimer. This method was further critically compared to high-level calculations recently reported in the literature for a range of pi-stacked complexes, including monosubstituted benzene-benzene dimers, along with DNA and RNA bases, and generally agrees with MP2 and/or CCSD(T) results to within +/-2 kJ mol(-1). We also show that the resulting BH&H binding energy is closely related to the electron density in the intermolecular region. The net result is that the BH&H functional, presumably due to fortuitous cancellation of errors, provides a pragmatic, computationally efficient quantum mechanical tool for the study of large pi-stacked systems such as DNA.     

Energetics of reactions involving radical species in solution: Calculation of relative electrode potentials for nitroimidazoles using density functional and continuum methods

Nonlocal density functional calculations and a semiempirical modified Born method for computing free energies of hydration were used to calculate the electrode potentials for a series of nitroimidazoles to a mean accuracy of about 80 mV. The density functional calculations used the nonlocal Becke '88 functional for exchange and either the nonlocal Lee-Yang-Parr or the local Vosko-Wilk-Nusair functionals for correlation and were performed at the HF/3-21G geometry. The most suitable geometry for these calculations was determined from a survey of various semiempirical, Hartree-Fock (HF) and density functional methods, with a variety of basis sets. The HF/3-21G method was found to yield a very favorable compromise between speed and accuracy in the determination of the geometry of 2-nitroimidazole, but the small basis set density functional calculations performed very badly. Density functional atom-optimized basis sets were found to give better overall results than traditional Pople-type basis sets. The free energy of hydration calculations employed the AM1 SM2 method. Both the gas-phase energies and the free energies of hydration made a significant contribution to the computed electrode potential. Indeed, an inverse relationship was found between the gas-phase electron affinity and the difference in free energy of hydration between the neutral nitroimidazole and its radical anion. The protocol established here may be useful for investigating novel bioreductive agents. © 1996 John Wiley & Sons, Inc.     

Self-consistent treatment of spin-orbit interactions with efficient Hartree-Fock and density functional methods

Efficient self-consistent field (SCF) schemes including both scalar relativistic effects and spin-orbit (SO) interactions at Hartree-Fock (HF) and density functional (DFT) levels are presented. SO interactions require the extension of standard procedures to two-component formalisms. Efficiency is achieved by using effective core potentials (ECPs) and by employing the resolution-of-the-identity approximation for the Coulomb part (RI-J) in pure DFT calculations as well as also for the HF-exchange part (RI-JK) in the case of HF or hybrid-DFT treatments. The procedures were implemented in the program system TURBOMOLE; efficiency is demonstrated for comparably large systems, such as Pb54. Relevance of SO effects for electronic structure and stability is illustrated by treatments of small Pb and Po clusters with and without accounting for SO effects.     

Hydrogen peroxide clusters: the role of open book motif in cage and helical structures

Hartree-Fock (HF) calculations using 6-31G*, 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets show that hydrogen peroxide molecular clusters tend to form hydrogen-bonded cyclic and cage structures along the lines expected of a molecule which can act as a proton donor as well as an acceptor. These results are reiterated by density functional theoretic (DFT) calculations with B3LYP parametrization and also by second-order M?ller-Plesset perturbation (MP2) theory using 6-31G* and 6-311++G(d,p) basis sets. Trends in stabilization energies and geometrical parameters obtained at the HF level using 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are similar to those obtained from HF/6-31G* calculation. In addition, the HF calculations suggest the formation of stable helical structures for larger clusters, provided the neighbors form an open book structure.     

Efficient hybrid density functional calculations in solids: assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional

The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree-Fock (HF) exchange used in the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2-4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.     

Seminumerical calculation of the Hartree-Fock exchange matrix: application to two-component procedures and efficient evaluation of local hybrid density functionals

A two-component extension of the seminumerical procedure for the calculation of the Hartree-Fock (HF) exchange matrix recently presented by Neese et al. (Chem Phys 2009, 356, 98) was implemented into the program system TURBOMOLE. It is demonstrated that this allows for efficient self-consistent treatment of spin-orbit coupling at HF and hybrid density functional theory level. One-component HF calculations were performed to study the accuracy of integration grids and the exploitation of the molecular point group symmetry. The efficiency was tested, and for one-component calculations compared to the implementation realized by Neese. It was further demonstrated that local hybrid density functionals can be evaluated with this technique. The "prototype" of this class of functionals, Lh-BLYP, was applied to an organic molecule with more than 150 atoms.     

Density functional theory study on the structure and vibrational frequencies of glycylglycine

Eleven possible conformers of glycylglycine have been studied by using the BLYP, B3LYP methods of density functional theory and the HF method at the basis set of 6-311++G**. BLYP (using Becke's and Lee-Yang-Parr's correlation functionals), ab initio Hartree-Fock (HF) and hybrid DFT/HF B3LYP calculations have been carried out to study the structure and vibrational spectra of glycylglycine. Glycylglycine crystal structure has been determined by X-ray diffraction analysis. The title compound has been crystallizes in the orthorhombic space group C1, with Z=4. And the unit cell parameters are: a=8.1184(12)A, b=9.5542(14)A, c=7.8192(11)A and V=577.95(15)A(3). Molecular conformation calculations have got 11 possible conformers. In these possible conformers, the most stable one has been selected. The BLYP/6-311++G** and scaled HF/6-311++G** frequencies correspond well with available experimental assignments of the normal vibrational modes. Comparison of the observed fundamental vibrational frequencies of glycylglycine and calculated results by density functional B3LYP and Hartree-Fock (HF) methods indicates that B3LYP is superior to the scaled Hartree-Fock (HF) for molecular vibrational issues.     

Quasiclassical trajectory calculations on the photodissociation of CF2CHCl at 193 nm: product energy distributions for the HF and HCl eliminations

Quasiclassical trajectory calculations were carried out to determine product energy distributions for the HCl and HF eliminations that take place in the photodissociation of 2-chloro-1,1-difluoroethylene at 193 nm. The trajectories were initiated at the transition states of the HCl and HF elimination channels under microcanonical, quasiclassical conditions, and were propagated with the energies and gradients taken directly from density functional theory calculations. Good agreement with experiment is found, except for the translational energy distribution of the HF elimination channel and the average vibrational energy of the HCl fragment. Possible sources of disagreement are discussed.     

Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

We present density functional theory (DFT) interaction energies for the sandwich and T‐shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree–Fock (HF) and second‐order Møller–Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene–dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

A comparative molecular field analysis (CoMFA) study using semiempirical, density functional, ab initio methods and pharmacophore derivation using DISCOtech on sigma 1 ligands

The Comparative Molecular Field Analysis (CoMFA) was developed to investigate a three-dimensional quantitative structure activity relationship (3D-QSAR) model of ligands for the sigma 1 receptor. The starting geometry of sigma-1 receptor ligands was obtained from the Tripos force field minimizations and conformations were decided from DISCOtech using the SYBYL 6.8. program. The structures of 48 molecules were fully optimized at the ab initio HF/3-21G* and semiempirical AM1 calculations using GAUSSIAN 98. The electrostatic charges were calculated using several methods such as semiempirical AM1, density functional B3LYP/3-21G*, and ab initio HF/3-21G*, MP2/3-21G* calculations within GAUSSIAN 98. Using the optimized geometries, the CoMFA results derived from the HF/3-21G method were better than those from AM1. The best CoMFA was obtained from HF/3-21G* optimized geometry and charges (R2 = 0.977). Using the optimized geometries, the CoMFA results derived from the HF/3-21G methods were better than those from AM1 calculations. The training set of 43 molecules gave higher R2 (0.989-0.977) from HF/3-21G* optimized geometries than R2 (0.966-0.911) values from AM1 optimized geometries. The test set of five molecules also suggested that HF/3-21G* optimized geometries produced good CoMFA models to predict bioactivity of sigma 1 receptor ligands but AM1 optimized geometries failed to predict reasonable bioactivity of sigma 1 receptor ligands using different calculations for atomic charges.     

Computational structural determination and energy landscape analysis of the hepatic carcinogen 2-(acetylamino)fluorene

 2-(Acetylamino)fluorene (AAF), a potent mutagen and a prototypical example of the mutagenic aromatic amines, forms covalent adducts to DNA after metabolic activation in the liver. A benchmark study of AAF is presented using a number of the most widely used molecular mechanics and semiempirical computational methods and models. The results are compared to higher-level quantum calculations and to experimentally obtained crystal structures. Hydrogen bonding between AAF molecules in the crystal phase complicates the direct comparison of gas-phase theoretical calculations with experiment, so Hartree–Fock (HF) and Becke–Perdew (BP) density functional theory (DFT) calculations are used as benchmarks for the semiempirical and molecular mechanics results. Systematic conformer searches and dihedral energy landscapes were carried out for AAF using the SYBYL and MMFF94 molecular mechanics force fields; the AM1, PM3 and MNDO semiempirical quantum mechanics methods; HF using the 3-21G*and 6-31G* basis sets; and DFT using the nonlocal BP functional and double numerical polarization basis sets. MMFF94, AM1, HF and DFT calculations all predict the same planar structures, whereas SYBYL, MNDO and PM3 all predict various nonplanar geometries. The AM1 energy landscape is in substantial agreement with HF and DFT predictions; MMFF94 is qualitatively similar to HF and DFT; and the MNDO, PM3 and SYBYL results are qualitatively different from the HF and DFT results and from each other. These results are attributed to deficiencies in MNDO, PM3 and SYBYL. The MNDO, PM3 and SYBYL models may be unreliable for compounds in which an amide group is immediately adjacent to an aromatic ring. Received: 26 May 2002 / Accepted: 12 December 2002 / Published online: 14 February 2003     

Acid-catalyzed isomerization of pivalaldehyde to methyl isopropyl ketone via a reactive protosolvated carboxonium ion intermediate.

Quantitative rearrangement of pivalaldehyde to methyl isopropyl ketone is observed in acids such as trifluoromethanesulfonic acid, anhydrous HF, and trifluoroethyl alcohol-BF3 but not in trifluoroacetic acid. Studies in a mixture of trifluoroacetic acid and trifluoromethanesulfonic acid show that acids with H(o) < or = -11 are able to carry out complete isomerization. These results and density functional theory calculations at the B3LYP/6-31G level suggest that protonated pivalaldehyde undergoes further protosolvation at higher acidities to a reactive superelectrophilic species resulting in rearrangement. A mechanism for the pivalaldehyde rearrangement to methyl isopropyl ketone in strong protic acids involving a reactive protosolvated superelectrophilic intermediate is suggested. Aspects of the related mechanism of the reaction with isobutane with CO in HF/BF3 medium leading to methyl isopropyl ketone are also discussed.     

Energy-adjusted pseudopotentials for the rare earth elements

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials and optimized (7s6p5d)/[5s4p3d]-GTO valence basis sets for use in molecular calculations for fixed f-subconfigurations of the rare earth elements, La through Lu, have been generated. Atomic excitation and ionization energies from numerical HF, as well as SCF pseudopotential calculations using the derived basis sets, differ by less than 0.1 eV from numerical HF all-electron results. Corresponding values obtained from CI(SD), CEPA-1, as well as density functional calculations using the quasirelativistic pseudopotentials, are in reasonable agreement with experimental data.     

Au(II)化合物[Au(CH2)2PH2]2X2 (X＝F, Cl, Br, I)的量子化学理论研究

采用从头计算HF, MP2方法和密度泛函理论, 对Au(II)系列化合物[Au(CH₂)₂PH₂]₂X₂ (X＝F, Cl, Br, I)的几何结构、电子结构和振动频率进行了研究. 研究表明Au的5d和6s电子参与Au—Au以及Au—X之间的成键. Au—Au, Au—X键强烈的电子相关作用使HF方法不适于该体系的研究, BP86和B3LYP两种泛函给出较大的Au—Au和Au—X键长, 而MP2方法和局域的密度泛函方法则给出了合理的结构参数. 局域密度泛函方法计算得到的Au—Au键和 Au—X键振动频率也与实验数据符合较好. 还运用含时密度泛函理论计算了[Au(CH₂)₂PH₂]₂X₂的电子激发能, 对分子在紫外-可见光谱范围内的电子跃迁进行了分析, 考察了卤素配体对激发能的影响, 并结合分子轨道能级的变化对此给予了解释.     

环己烯分子2b和3a轨道的电子动量谱学研究

The electron momentum profile for inner valence orbitals 2b and 3a of cyclohexene (C6H10) was firstly studied by the binary (e,2e) electron momentum spectroscopy (EMS), at the impact energy of 1200 eV plus binding energy using symmetric non-coplanar kinematics. The complete valence shell binding energy spectrum of C6H10 was also obtained. The experimental momentum profile of the summed orbitals was compared with Hartree Fock (HF) and density functional theory (DFT) methods with various basis sets. The experimental measurement was well described by the HF and DFT calculations except for the low-p region (p<0.25 a.u.). Experimental small “turn-up” effects of momentum profile in the low-p region could be due to the distorted wave effects.     

Structural Characteristics of Graphane‐Type C and BN Nanostructures by Periodic Local MP2 Approach

The structural characteristics of fully‐hydrogenated carbon and boron nitride mono‐ and multilayer slabs, together with nanotubes derived from the slabs, are investigated mainly by means of periodic local second‐order Møller–Plesset perturbation (LMP2) calculations and the results are compared with Hartree–Fock (HF), density functional theory (DFT), and dispersion function‐augmented DFT (DFT‐D) obtained ones. The investigated systems are structurally analogous to (111) and (110) slabs of diamond, where the hydrogenated (111) slab of diamond corresponds to the experimentally known graphane. Multilayering of monolayers and nanotubes is energetically favorable at the LMP2 level for both C and BN, while HF and DFT are not able to reproduce this behavior for CH systems. The work highlights the importance of utilizing methods capable of properly describing weak interactions in the investigation of dispersively‐bound systems such as the multilayered graphanes and the corresponding nanotubes.     

Infrared and Raman spectra and theoretical study of methyl trifluoromethyl sulfone, CF3SO2CH3

The infrared and Raman spectra were obtained for liquid CF3SO2CH3, as well as the infrared spectrum of the gaseous substance. The molecular geometry was optimized by means of the Hartree-Fock (HF), second order electron correlation (MP2) and density functional theory (DFT) procedures of quantum chemistry, resulting in a structure with Cs symmetry. The wavenumbers corresponding to the normal modes of vibration were calculated using the DFT (B3LYP/6-31G**) approximation and their agreement with the measured values improved after scaling of the associated force field. An assignment of bands is proposed on the basis of such calculations and the comparison with related molecules.