Direct inversion of the iterative subspace with contracted planewave basis functions

Ways to reduce the computational cost of periodic electronic structure calculations by using basis functions corresponding to linear combinations of planewaves have been examined recently. These contracted planewave (CPW) basis functions correspond to Fourier series representations of atom‐centered basis functions, and thus provide access to some beneficial properties of planewave (PW) and localized basis functions. This study reports the development and assessment of a direct inversion of the iterative subspace (DIIS) method that employs unique properties of CPW basis functions to efficiently converge electronic wavefunctions. This method relies on access to a PW‐based representation of the electronic structure to provide a means of efficiently evaluating matrix–vector products involving the application of the Fock matrix to the occupied molecular orbitals. These matrix–vector products are transformed into a form permitting the use of direct diagonalization techniques and DIIS methods typically employed with atom‐centered basis sets. The abilities of this method are assessed through periodic Hartree–Fock calculations of a range of molecules and solid‐state systems. The results show that the method reported in this study is approximately five times faster than CPW‐based calculations in which the entire Fock matrix is calculated. This method is also found to be weakly dependent upon the size of the basis set, thus permitting the use of larger CPW basis sets to increase variational flexibility with a minor impact on computational performance. © 2018 Wiley Periodicals, Inc.     

An analysis of the topology of the electron charge density and the reactant–product electronic structure variation along the intrinsic reaction coordinate

In this work the topology of the electron charge density and the variations in the reactant and product electronic structures are analyzed along the Fukui intrinsic reaction coordinate (IRC). The systems studied are the ionic and the Menschutkin S_N2 reactions. This study is performed at ab initio RHF and MP2 levels, and density functional level, employing the B3LYP functional. The basis set in all cases is of split valence type and includes diffuse and polarization functions in nonhydrogen atoms 6‐31+G*. As a measure of the variations of reactant and product electronic structures, we calculate at the RHF level, the overlap integral between the total wavefunction and the wavefunction based on the reactant (or product) localized fragment orbitals. This integral can be interpreted, in Hilbert space, as the cosine of the angle between the vector representing the electronic structure of the molecule in each point of the IRC and that of reactant (or product) electronic structure. The calculated molecular properties were analyzed in light of the valence bond approach, and qualitative differences were noted depending on the property studied. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Diagonal coefficient representation of density functions and quantum similarity measures

Quantum similarity measures within a new theoretical point of view are described for arbitrary order density functions, with the aid of attached pseudo-wave functions, in a vector semispace structure associated with a Minkowski metric.     

三聚氰胺对金属(Ⅱ)卟啉反应活性影响的概念密度泛函研究

选取8个典型的二价金属卟啉MP(M=Ca,Mg,Zn,Cu,Ni,Fe,Co,Mn)与三聚氰胺(L)形成轴向金属配合物(L-MP),应用概念密度泛函工具,系统地计算和比较了L键合前后对其结构和反应性质的影响.结果表明:除钙的特别不稳定物外,L配体对其余6种MP的结构影响较小,它们有较高的化学势指数和较低的总化学硬度而趋向配体的解离;与铁卟啉能形成最稳定的轴向配合物,电子由配体N原子流向铁,中心铁的亲核Fukui指数值大于体系里其他原子的Fukui指数,且发生符号改变.在这些典型的赤道键合配合物中,金属M、配体N之间的二级微扰相互作用能,自然电荷布局以及概念密度泛函指数等方面,存在着一系列线性关系.以上结果可为体内三聚氰胺致结石提供新的启示.     

Density functional theory study on the interaction between metalloporphyrins and NH3

The binding behaviors of eight bivalent metalloporphyrins (MPs) (M?Zn, Mg, Cu, Mn, Fe, Co, Ni, and Cd) with NH₃ were investigated by density functional theory. For both MPs and corresponding complexes MPs‐NH₃, good linear correlations are found between the partial charge on metal M and that on atom N (nitrogen of porphyrin) as well as the M? N bond length. Natural population and frontier orbital analysis demonstrate that charge transfer in CoP‐NH₃ is much easier and greater. As a consequence of the charge transfer and the hybridization of molecular energy levels, striking disparities of electronic properties of MPs‐NH₃ are observed. Particularly, a modest linear relationship is obtained between the magnitude of charge transfer and the binding energy. The much greater Fukui functions of CoP, together with its larger binding strength, suggest that CoP is more favorable to the interaction with NH₃, which might be a promising sensing material to response NH₃. © 2013 Wiley Periodicals, Inc.     

Newly developed basis sets for density functional calculations

Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.     

Representation of square-cell configurations in the complex plane: Tools for the characterization of molecular monolayers and cross sections of molecular surfaces

Two numerical codes, a complex face vector F and a real face vector D are developed for the characterization of square-cell configurations (lattice animals), used for representing the shapes of molecular monolayers and cross sections of molecular surfaces. The real face vector D represents all the intrinsic properties, size, and shape of the lattice animal. The complex face vector F contains complete information about the size, the shape, and also the placement of the particular lattice animal with respect to the lattice. Based on the properties of the face vectors, a method is developed for the classification of similar animals into equivalence classes. The face vector method is proposed for an algorithmic, nonvisual computer analysis of similarity of shapes of molecular monolayers and planar domains of cross sections of molecular surfaces, approximated by lattice animals.     

Negative and Infinite Fukui Functions: The Role of Diagonal Dominance in the Hardness Matrix

The possible genesis of negative atom condensed Fukui functions is discussed based on hardness kernel matrix relationships. The recent hypothesis that diagonal dominance of the hardness matrix is a requirement for positive Fukui functions is proven, and general considerations also predict the possibility of regions with numerically unstable Fukui functions, including discontinuities.     

Effect of temperature and pressure on the structure, dynamics, and hydrogen bond properties of liquid N-methylacetamide: a molecular dynamics study

The structure and dynamical properties of liquid N-methylacetamides (NMA) are calculated at five different temperatures and at four different pressures using classical molecular dynamics simulations. Our results are analyzed in terms of pressure-induced changes in structural properties by investigating the radial distribution functions of different atoms in NMA molecule. It is found that the first peak and also the second peak of C-O and N-H are well defined even at higher temperature and pressure. It is also observed that the number of hydrogen bonds increase with application of pressure at a given temperature. On the other hand, the calculated hydrogen bond energy (E(HB)) shows that the stability of hydrogen bond decreases with increasing of pressure and temperature. Various dynamical properties associated with translational and rotational motion of neat NMA are calculated and the self-diffusion coefficient of NMA is found to be in excellent agreement with the experiment and the behavior is non-Arrhenius at low temperatures with application of pressures. The single particle orientational relaxation time for dipole vector and N-C vector are also calculated and it is found that the orientational relaxation time follows Arrhenius behavior with a variation of temperature and pressure.     

Strong intramolecular hydrogen bonds. Part I. Vibrational frequencies of the OH group in some picolinic acid N-oxides predicted from DFT calculated potentials and located in the infrared spectra

Hydrogen bonding in picolinic acid N-oxide (I), its 4-nitro (III), 4-methoxy (IV), 4-amino (V) derivatives and in quinaldic acid N-oxide (II) was characterized by calculations (B3LYP/6-31G(d)) of metric parameters, H-bond energies and one-dimensional proton potential functions with vibrational energy levels. Solvent effects were estimated by the SCRF PCM method of Tomasi and coworkers (J. Tomasi, M. Persico, Chem. Rev. 94 (1994) 2027). The potential functions are strongly asymmetric with the energy minimum placed near the carboxylic oxygen. The inflection near the NO oxygen develops into a second, shallower minimum under the SCRF.

Empirical assignments of the OH stretching and bending modes were made for (I)–(IV). The stretchings of (I, II) and (IV) in various solvents are observed in the region 1600–1300 cm⁻¹, but near 2600 cm⁻¹ for (III). The calculated and observed frequencies are in fairly good agreement with theoretical predictions reflecting the electronic effects of the substituents upon the H-bond strength. The observed trends in the solvent effects upon various parameters characterizing the H-bonding also correspond to predictions.     

Erratum: On equilibrium intensive thermodynamic properties of composed p‐particles in many‐body systems*

Equilibrium intensive thermodynamic properties of p‐particles (p‐ons), i.e., composed particles formed by few particles of the same nature such as fermion or boson pairs (p=2), trios (p=3), etc., are investigated. The relation of the p‐particle correlation functions to its p‐hole counterparts and an existing covariant structure in the hierarchy of the p‐particle correlation functions allow these generalized intensive properties to be properly defined and characterized. The connection between these generalized properties of the composed objects and those of the components is also derived. An explicit derivation of the chemical potential for pairs and its generalization to p‐particles is performed. Such results are further extended to any intensive property. Finally, the present development allows some previous results to be clearly interpreted thus yielding an important support for our theory. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

On equilibrium intensive thermodynamic properties of composed p‐particles in many‐body systems

Equilibrium intensive thermodynamic properties of p‐particles (p‐ons), i.e., composed particles formed by few particles of the same nature such as fermion or boson pairs (p=2), trios (p=3), etc., are investigated. The relation of the p‐particle correlation functions to its p‐hole counterparts and an existing covariant structure in the hierarchy of the p‐particle correlation functions allow these generalized intensive properties to be properly defined and characterized. The connection between these generalized properties of the composed objects and those of the components is also derived. An explicit derivation of the chemical potential for pairs and its generalization to p‐particles is performed. Such results are further extended to any intensive property. Finally, the present development allows some previous results to be clearly interpreted thus yielding an important support for our theory. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 85: 63–71, 2001     

Nuclear attraction and electron interaction integrals of exponentially decaying functions and the Poisson equation

Summary The technique proposed by O-Ohata and Ruedenberg (J Math Phys 7:547 (1966)) and by Silver and Ruedenberg (J Chem Phys 49:4306 (1968)) of computing nuclear attraction and electron interaction integrals by solving an inhomogeneous Laplace equation can also be applied ifB functions (Filter E, Steinborn EO (1978) Phys Rev A 18:1) are used as basis functions in atomic and molecular calculations. It is shown that because of the remarkable mathematical properties ofB functions the derivation of compact explicit expressions for the multicenter integrals mentioned above is particularly simple. These results are also of interest in the context of other exponentially decaying functions, since all the other commonly occurring exponentially decaying functions as, for instance, Slater functions or bound state hydrogen eigenfunctions can be expressed as simple linear combinations ofB functions. Consequently, their multicenter integrals can also be expressed in terms of multicenter integrals ofB functions.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

Structure and Stability of TaON Polymorphs

The stabilities and electronic structures of several polymorphs of tantalum oxynitride, TaON, were studied quantum‐chemically at density‐functional level. Results obtained by complementary quantum‐chemical techniques with wave‐functions either expanded in atom‐centered functions or in plane waves were compared. Close agreement was obtained for the relative stabilities of the baddeleyite, anatase, rutile, and fluorite phases of TaON. The effect of anion distribution on the structural parameters and the lattice energies of the anatase and rutile polymorphs was investigated. The calculated band structure of the polymorphs is compared with available experimental information.     

Spectroscopic,quantum computational and molecular docking studies on 1-phenylcyclopentane carboxylic acid

The vibrational wavenumbers of optimized molecular structure of 1-phenylcyclopentane carboxylic acid (1PCPCA) molecule have been calculated by quantum chemical theory and compared with experimental results. The density functional theory (DFT) approach is followed using the method B3LYP and 6-311++G(d,p) basis set. Using potential energy distribution, all the assignments of the basic vibrational modes were calculated. Natural bond orbital (NBO) and atoms in molecules (AIM) topological studies applied to get the intermolecular interactions of the compound. ¹H and ¹³C chemical shift of NMR was estimated on the molecule and also compared with the experimental spectra. In order to find the band gap, the time-dependent (TD-DFT) method is used to get the higher order energy levels properties and also compared with experimental data of UV–vis spectrum. From the analysis of various spectroscopic studies, there is a good relationship between the experimental and theoretical values obtained. Quantum characters, bio-active nature and reactive areas of the molecule are revealed by Fukui function, molecular electrostatic potential (MEP) and Hirshfeld surface studies. The human enzyme steroidogenic types and their protein targets were tested with this molecule by molecular docking.     

2,4-Ditellurouracil and its 5-fluoro derivative: Theoretical investigations of structural,energetics and ADME parameters

2,4-Ditellurouracil exhibits keto-enol tautomerism via different pathways resulting in seven tautomers. These pathways were studied in the gas phase using density functional theory method. The functionals used were BLYP, B3LYP and BHLYP and the basis sets were 6–311++G(d,p) for all atoms except that LanL2DZ ECP was used for tellurium atom only. The results indicate that the diketo form is more stable as observed for uracil and its sulfur and selenium analogues. The effect of introducing fluorine at position 5 was also investigated and the energy difference between the diketo and dienol forms is reduced. 2,4-Ditellurouracil and its 5-fluoro analogue are expected to exist exclusively as the diketo form due to the high interconversion energy barrier. We extended the investigation to predict ADME parameters of the most stable diketo and dienol tautomers in view of understanding their biological properties. This research enlightens keto-enol tautomerism of 2,4-ditellurouracil and its 5-fluoro derivative with additional insights to biological functions.     

Shape-persistency and molecular function in heteromacrocycles: creation of heteroarenecyclynes and arene-azaarenecyclynes

On the basis of our concept that the introduction of heteroatoms and shape-persistency into the pi-macrocycles should bring forth striking functions or properties, heteroarenecyclynes (such as oxaarenecyclynes and thiaarenecyclynes) with semi-shape-persistent structure, and arene-azaarenecyclynes with shape-persistent structure have been prepared. Their novel functions and characteristic properties are disclosed. Noteworthy is that heteroarenecyclynes include C(60) to provide a Saturn-type complex with a N(2) binding function. A simple member of the oxaarenecyclyne compounds undergoes the Ag(I)-induced cyclization leading to the quantitative formation of strongly luminescent perylene derivative. Arene-azaarenecyclynes are versatile compounds. For example, they exhibit intense luminescence in spite of the meta-bonding structure, providing the circular luminophore. Also they serve as receptors for special metal, organic, and inorganic substrates. The observed molecular functions are valuable for scientific and practical application.     

TiP2^+,TiP4^+,Ti2P4^+二元团簇的理论研究

利用含有电子相关效应校正的密度泛函理论DFT中的B3LYP方法,选择LANL2DZ双ξ基组,并考虑极化函数,对TiP2^+,TiP4^+,Ti2P4^+二元团簇各种可能存在的几何构型及电子结构进行了密度泛函理论研究,得到了TimPn^+二元团族的最稳定构型,其中TiP2^+的最稳定构型为C2v对称性的三角形,TiP4^+的最稳定构型亦具有C2v对称性,Ti2P4^+的最稳定构型为具有D2d对称性的共边双四面体,所得构型很好地说明了激光光解的实验结果。     

Structure, bonding and physical properties of tetragonal and orthorhombic SiS2 from (hybrid) DFT calculations

The energetics, structure and physical properties of tetragonal and orthorhombic SiS₂ were calculated by periodic density functional theory (DFT) calculations, using both localized orbital and projected augmented wave basis-sets. All methods applied agree upon the relative energies of the different polymorphs but show differences in the predicted geometries, which are minimized upon improving the basis-set quality. The hybrid PBE0 functional was found to give the best match between experimental and calculated structures. When comparing SiS₂ with its much better studied oxide analog silica, we observe that upon substituting sulphur for oxygen, the energy landscape changes dramatically. Other effects of changing S for O are found to be smaller Si-X-Si angles, a broader distribution of X-Si-X angles, a more flexible framework and a significantly reduced band gap. The latter is in line with the experimental observation of photoluminescence in related GaGeS₂ compounds and suggests that SiS₂ might find application in UV light emitting diodes. Finally, a comparison of the maximally localized Wannier functions demonstrates that the Si-S bonds in SiS₂ have a considerably more covalent character than the Si-O bonds in silica.     

Exact finite series for the few-body auxiliary functions

The so-called few-body auxiliary functions play a very important role in bound-state calculations for nonrelativistic few-body systems. In particular, the functions of the first, second, and third orders are used in four-body calculations. By means of an original approach developed for the first time in the present study, we have found exact finite-series representations for the auxiliary functions A_n (n ≤ 3). It is shown that the auxiliary functions A_n are closely related to the Gaussian hypergeometric function ₂F₁. A few simple finite-series expansions are also presented, which seem to be very convenient for numerical computations. This work opens a new avenue in the study of auxiliary functions and their properties. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 269–278, 1997